2024-03-29T09:00:11Zhttps://idus.us.es/oai/requestoai:idus.us.es:11441/236062019-03-12T11:55:26Zcom_11441_10803com_11441_10802com_11441_10690com_11441_10893col_11441_10804col_11441_10896
00925njm 22002777a 4500
dc
2005
Let $f_1,\ldots, f_p$ be polynomials in ${\bf C}[x_1,\ldots, x_n]$
and let $D = D_n$ be the $n$-th Weyl algebra. The annihilating
ideal of $f^s=f_1^{s_1}\cdots f_p^{s_p}$ in
$D[s]=D[s_1,\ldots,s_p]$ is a necessary step for the computation
of the Bernstein-Sato ideals of $f_1,\ldots, f_p$.
We point out experimental differences among the efficiency of the
available methods to obtain this annihilating ideal and provide
some upper bounds for the complexity of its computation.
978-3-540-28966-1
http://hdl.handle.net/11441/23606
https://idus.us.es/xmlui/handle/11441/23606
Bernstein-Sato ideals
Nouvelle Cuisine for the Computation of the Annihilating Ideal of $f^s$
oai:idus.us.es:11441/422862024-02-14T19:31:18Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2002-04
We prove that the pure braid groups on compact, connected, orientable surfaces are bi-orderable, and that the pure braid groups on compact, connected non-orientable surfaces have generalized torsion, thus they are not bi-orderable.
González-Meneses López, J. (2002). Ordering pure braid groups on compact, connected surfaces. Pacific Journal of Mathematics, 203 (2), 369-378.
0030-8730
1945-5844
http://hdl.handle.net/11441/42286
http://dx.doi.org/10.2140/pjm.2002.203.369
https://idus.us.es/xmlui/handle/11441/42286
Ordering pure braid groups on compact, connected surfaces
oai:idus.us.es:11441/1386542024-02-14T13:24:45Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2015-03-14
Many problems in engineering design involve the use of nonlinearities and
some integer variables. Methods based on test sets have been proposed to solve some
particular problems with integer variables, but they have not been frequently applied
because of computation costs. The walk-back procedure based on a test set gives an
exact method to obtain an optimal point of an integer programming problem with linear
and nonlinear constraints, but the calculation of this test set and the identification of
an optimal solution using the test set directions are usually computationally intensive.
In problems for which obtaining the test set is reasonably fast, we show how the
effectiveness can still be substantially improved. This methodology is presented in its
full generality and illustrated on two specific problems: (1) minimizing cost in the
problem of scheduling jobs on parallel machines given restrictions on demands and
capacity, and (2) minimizing cost in the series parallel redundancy allocation problem,
given a target reliability. Our computational results are promising and suggest the applicability of this approach to deal with other problems with similar characteristics
or to combine it with mainstream solvers to certify optimality.
0926-6003
1573-2894
https://hdl.handle.net/11441/138654
10.1007/s10589-015-9739-3
Non-linear integer programming
Test set
Gröbner basis
Chance constrained programming
An improved test set approach to nonlinear integer problems with applications to engineering design
oai:idus.us.es:11441/411642024-02-13T09:20:19Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2014
In this note we solve the twisted conjugacy problem for braid
groups, i.e. we propose an algorithm which, given two braids u, v ∈ Bn and
an automorphism ϕ ∈ Aut(Bn), decides whether v = (ϕ(x))−1ux for some
x ∈ Bn. As a corollary, we deduce that each group of the form Bn o H, a
semidirect product of the braid group Bn by a torsion-free hyperbolic group
H, has solvable conjugacy problem.
González-Meneses López, J. y Ventura Capell, E. (2014). Twisted conjugacy in braid groups. Israel Journal of Mathematics, 201 (1), 455-476.
0021-2172
1565-8511
http://hdl.handle.net/11441/41164
http://dx.doi.org/10.1007/s11856-014-0032-4
https://idus.us.es/xmlui/handle/11441/41164
Braid group
twisted conjugacy
Twisted conjugacy in braid groups
oai:idus.us.es:11441/1391392024-02-14T08:44:59Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
1996-08
We prove that if D is a "strongly quasihomogeneous" free divi-
sor in the Stein manifold X, and U is its complement, then the de Rham
cohomology of U can be computed as the cohomology of the complex of mero-
morphic differential forms on X with logarithmic poles along D, with exterior
derivative. The class of strongly quasihomogeneous free divisors, introduced
here, includes free hyperplane arrangements and the discriminants of stable
mappings in Mather's nice dimensions (and in particular the discriminants of
Coxeter groups).
Castro Jiménez, F.J., Narváez Macarro, L. y Mond, D. (1996). Cohomology of the complement of a free divisor. Transactions of the American Mathematical Society, 348 (8), 3037-3049.
0002-9947
1088-6850
https://hdl.handle.net/11441/139139
Cohomology of the complement of a free divisor
oai:idus.us.es:11441/420182024-02-14T13:55:06Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2005
We give some estimates for multiplicative character sums on quasiprojective
varieties over finite fields depending on the severity of the singularities of the variety at infinity. We also remove the hypothesis of non-divisibility by the characteristic of the base field in the known estimates for the non-singular case.
Rojas León, A. (2005). Estimates for singular multiplicative character sums. International Mathematics Research Notices, 2005, 1221-1234.
1073-7928
1687-0247
http://hdl.handle.net/11441/42018
http://dx.doi.org/10.1155/IMRN.2005.1221
https://idus.us.es/xmlui/handle/11441/42018
Estimates for singular multiplicative character sums
oai:idus.us.es:11441/1547132024-02-06T13:32:43Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2023-05-03
This work highlights the existence of partial symmetries in large families of iterated plethystic coefficients. The plethystic coefficients involved come from the expansion in the Schur basis of iterated plethysms of Schur functions indexed by one-row partitions.The partial symmetries are described in terms of an involution on partitions, the flip involution, that generalizes the ubiquitous � involution. Schur-positive symmetric functions possessing this partial symmetry are termed flip-symmetric. The operation of taking plethysm with �� preserves flip-symmetry, provided that � is a partition of two. Explicit formulas for the iterated plethysms �2∘��∘�� and ��∘�2∘��, with a, b, and c ≥ 2 allow us to show that these two families of iterated plethysms are flip-symmetric. The article concludes with some observations, remarks, and open questions on the unimodality and asymptotic normality of certain flip-symmetric sequences of iterated plethystic coefficients.
Gutiérrez Cáceres, Á. y Rosas Celis, M.H. (2023). Partial symmetries of iterated plethysms. Annals of Combinatorics, 27 (3), 493-518. https://doi.org/10.1007/s00026-023-00652-4.
0218-0006
0219-3094
https://hdl.handle.net/11441/154713
10.1007/s00026-023-00652-4
Symmetric functions
Plethysm
Partial symmetries of iterated plethysms
oai:idus.us.es:11441/484422024-02-13T09:21:41Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2011
In this paper we obtain realizations of the 4-dimensional general
symplectic group over a prime field of characteristic ℓ > 3 as the Galois
group of a tamely ramified Galois extension of Q. The strategy is to consider the Galois representation ρℓ attached to the Tate module at ℓ of a suitable abelian surface. We need to choose the abelian varieties carefully in order to ensure that the image of ρℓ is large and simultaneously maintain a control on the ramification of the corresponding Galois extension. We obtain an explicit family of curves of genus 2 such that the Galois representation attached to the ℓ-torsion points of their Jacobian varieties provide tame Galois realizations of the desired symplectic groups.
Arias de Reyna Domínguez, S. y Vila Oliva, N. (2011). Tame Galois realizations of GSp4 (Fℓ) over Q. International Mathematics Research Notices, 2011 (9), 2028-2046.
1073-7928
1687-0247
http://hdl.handle.net/11441/48442
10.1093/imrn/rnq144
https://idus.us.es/xmlui/handle/11441/48442
Tame Galois realizations of GSp4 (Fℓ) over Q
oai:idus.us.es:11441/466062016-11-29T12:18:29Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2003
Rosas Celis, M.H. (2003). Los números de (Euler)-Catalan. Boletín de la Asociación Matemática Venezolana, 10 (1), 43-58.
1315-4125
http://hdl.handle.net/11441/46606
https://idus.us.es/xmlui/handle/11441/46606
Los números de (Euler)-Catalan
oai:idus.us.es:11441/235992024-02-15T07:20:53Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2003-12
Let $A_n(k)$ be the Weyl algebra, with $k$ a field of characteristic zero.
It is known that every projective finitely generated left module is free
or isomorphic to a left ideal. Let $M$ be a left submodule of a free
module. In this paper we give an algorithm to compute the projective
dimension of $M$. If $M$ is projective and $\rk(M) \ge 2$ we give a
procedure to find a basis.
Gago Vargas, M.J. (2003). Bases for Projective modules in An(k). Journal of Symbolic Computation, 36 (6), 845-853.
0747-7171
http://hdl.handle.net/11441/23599
https://idus.us.es/xmlui/handle/11441/23599
Projective modules
non commutative rings
Gröbner bases
Bases for Projective modules in An(k)
oai:idus.us.es:11441/1447902024-02-13T09:07:11Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2021-06-29
We give an almost complete classification of Artin groups of spherical
type up to commensurability. Let A and A0 be two Artin groups of spherical type,
and let A1; : : : ; Ap (respectively, A0
1; : : : ; A0
q) be the irreducible components of A
(respectively, A0). We show that A and A0 are commensurable if and only if p D q
and, up to permutation of the indices, Ai and A0
i are commensurable for every i . We
prove that, if two Artin groups of spherical type are commensurable, then they have
the same rank. For a fixed n, we give a complete classification of the irreducible Artin
groups of rank n that are commensurable with the group of type An. Note that there
are six remaining comparisons of pairs of groups to get the complete classification of
Artin groups of spherical type up to commensurability, two of which have been done
by Ignat Soroko after the first version of the present paper.
Cumplido Cabello, M. y Paris, L. (2021). Commensurability in Artin groups of spherical type. REVISTA MATEMATICA IBEROAMERICANA, 38 (2), 503-526. https://doi.org/10.4171/RMI/1282.
0213-2230
https://hdl.handle.net/11441/144790
10.4171/RMI/1282
Commensurability in Artin groups of spherical type
oai:idus.us.es:11441/419502024-02-14T11:45:27Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2006
In this paper we study elliptic curves which have a number of points whose coordinates are in arithmetic progression. We first motivate this diophantine problem, prove some results, provide a number of interesting examples and, finally point out open questions which focus on the most interesting aspects of the problem for us.
García Selfa, I. y Tornero Sánchez, J.M. (2006). On simultaneous arithmetic progressions on elliptic curves. Experimental Mathematics, 15 (4), 471-478.
1058-6458
1944-950X
http://hdl.handle.net/11441/41950
10.1080/10586458.2006.10128979
https://idus.us.es/xmlui/handle/11441/41950
Elliptic curves
arithmetic progressions
On simultaneous arithmetic progressions on elliptic curves
oai:idus.us.es:11441/466012024-02-13T22:09:18Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2008
Tanisaki introduced generating sets for the defining ideals of the schematic intersections of the closure of conjugacy classes of nilpotent matrices with the set of diagonal matrices. These ideals are naturally labeled by integer partitions. Given such a partition λ, we define several methods to produce a reduced generating set for the associated ideal Iλ. For particular shapes we find nice generating sets. By comparing our sets with some generating sets of Iλ arising from a work of Weyman, we find a counterexample to a
related conjecture of Weyman.
Biagioli, R., Faridi, S. y Rosas Celis, M.H. (2008). The defining ideals of conjugacy classes of nilpotent matrices and a conjecture of Weyman. International Mathematics Research Notices, 2008, 117-1-117-33.
1073-7928
1687-0247
http://hdl.handle.net/11441/46601
10.1093/imrn/rnn117
https://idus.us.es/xmlui/handle/11441/46601
The defining ideals of conjugacy classes of nilpotent matrices and a conjecture of Weyman
oai:idus.us.es:11441/475812024-02-14T20:37:26Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2011-07-15
Let us consider an equation of the form P(x, z) = zm + w1(x)zm−1 + · · · + wm−1(x)z + wm(x) = 0, where m>1, n>1, x=(x1⋯xn) is a vector of variables, k is an algebraically closed field of characteristic zero, View the MathML source and wm(x)≠0. We consider representations of its roots as generalized Puiseux power series, obtained by iterating the classical Newton procedure for one variable. The key result of this paper is the following:
Theorem 1.The iteration of the classical Newton procedure for one variable gives rise to representations of all the roots of the equation above by generalized Puiseux power series in x1/d, d∈Z>0, whose supports are contained in an n-dimensional, lex-positive strictly convex polyhedral cone (see Section 5). We must point out that the crucial result is not the existence of these representations, which is a well-known fact; but the fact that their supports are contained in such a special cone. We achieve the proof of this theorem by taking a suitable affine chart of a toric modification of the affine space.
Soto Prieto, M.J. y Vicente Córdoba, J.L. (2011). The Newton Procedure for several variables. Linear Algebra and its Applications, 435 (2), 255-269.
0024-3795
http://hdl.handle.net/11441/47581
10.1016/j.laa.2011.01.033
https://idus.us.es/xmlui/handle/11441/47581
Newton procedure
Generalized Puiseux Series
Monomial blowing-up
Toric modifications
The Newton Procedure for several variables
oai:idus.us.es:11441/1546992024-02-12T11:20:52Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2015-08-28
The reduced Kronecker coefficients are particular instances of Kronecker coefficients, that nevertheless contain enough information to compute all Kronecker coefficients from them. In this note, we compute the generating function of a family of reduced Kronecker coefficients. We show that these reduced Kronecker coefficients count plane partitions. This allows us to check that these coefficients satisfy the saturation conjecture, and that they are weakly increasing. Thanks to its generating function, we can describe our family by a quasipolynomial, specifying its degree and period.
Les coefficients de Kronecker réduits sont des coefficients de Kronecker particuliers, qui permettent néanmoins de recalculer tous les coefficients de Kronecker. Dans cette note, nous calculons la fonction génératrice d’une famille particulière de coefficients de Kronecker réduits. Nous exprimons sa relation avec les partitions planes, ce qui nous permet de vérifier que cette famille possède la propriété de saturation, ainsi que la propriété de monotonie. Grâce à cette fonction génératrice, nous pouvons décrire les coefficients considérés au moyen d’une formule quasi polynomiale, dont nous précisons le degré et la période.
Colmenarejo Hernando, L. y Rosas Celis, M.H. (2015). Combinatorics on a family of reduced Kronecker coefficients. Comptes Rendus Mathématique, 353 (10), 865-869. https://doi.org/10.1016/j.crma.2015.07.012.
1631-073X
1778-3569
https://hdl.handle.net/11441/154699
10.1016/j.crma.2015.07.012
Combinatorics on a family of reduced Kronecker coefficients
oai:idus.us.es:11441/430842019-04-03T06:09:20Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2001
In this paper, we give a new proof of the continuity of division by differential operators with analytic coefficients, originally proved by Mebkhout and the second author. Our methods come from the proof of the Constant Rank Theorem for analytic maps between power series spaces, given by Müller and the first author.
Hauser, H. y Narváez Macarro, L. (2001). Continuous division of differential operators. Annales de l'Institut Fourier, 51 (3), 769-778.
0373-0956
1777-5310
http://hdl.handle.net/11441/43084
http://dx.doi.org/10.5802/aif.1836
https://idus.us.es/xmlui/handle/11441/43084
differential operators
division theorems
continuity
Continuous division of differential operators
oai:idus.us.es:11441/462442024-02-14T20:22:55Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
1999
We prove a structure theorem for differential operators in the 0-th term of the V-filtration relative to a free divisor. manifold. As an application, we give a formula for the logarithmic de Rham complex with respect to a free divisor in terms of V0-modules, which generalizes the classical formula for the usual de Rham complex in terms of D-modules, and the formula of Esnault-Viehweg in the case of a normal crossing divisor. We also give a sufficient algebraic condition for perversity of the logarithmic de Rham complex.
Nous prouvons un théorème de structure pour les opérateurs différentiels dans le terme 0 de la V-filtration relative à un diviseur libre. Comme application, nous donnons une formule pour le complexe de de Rham logarithmique par rapport à un diviseur libre en termes de V0-modules, qui généralise la formule classique pour le complexe de de Rham usuel en termes de D-modules et celle de Esnault-Viehweg dans le cas d'un diviseur à croisements normaux. Nous donnons aussi une condition algébrique suffisante pour la perversité des tels complexes.
Calderón Moreno, F.J. (1999). Logarithmic differential operators and logarithmic de Rham complexes relative to a free divisor. Annales Scientifiques de l'École Normale Supérieure, 32 (5), 701-714.
0012-9593
http://hdl.handle.net/11441/46244
10.1016/S0012-9593(01)80004-5
https://idus.us.es/xmlui/handle/11441/46244
Logarithmic differential operators and logarithmic de Rham complexes relative to a free divisor
oai:idus.us.es:11441/420482024-02-14T08:59:55Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2015
A modified A-hypergeometric system is a system of differential equations for the function f(t w · x) where f(y) is a solution of an A-hypergeometric system in n variables and w is an n dimensional integer vector, which is called the weight vector. We study the irregularity of modified systems by adapting to this case the notion of umbrella introduced by M. Schulze and U. Walther. Especially, we study slopes and Gevrey series solutions. We develop some applications of this study. Under some conditions we give Laplace integral representations of divergent series solutions of the modified system and we show that certain Gevrey series solutions of the original A-hypergeometric system along coordinate varieties are Gevrey asymptotic expansions of holomorphic solutions of the A-hypergeometric system.
Castro Jiménez, F.J., Fernández Fernández, M.C., Koike, T. y Takayama, N. (2015). Irregular modified A-Hypergeometric systems. Transactions of the American Mathematical Society, 367 (8), 5415-5445.
0002-9947
1088-6850
http://hdl.handle.net/11441/42048
10.1090/S0002-9947-2014-06225-9
https://idus.us.es/xmlui/handle/11441/42048
Irregular modified A-Hypergeometric systems
oai:idus.us.es:11441/411582024-02-13T09:53:44Zcom_11441_10893com_11441_10802com_11441_10690com_11441_10803col_11441_10894col_11441_10804
00925njm 22002777a 4500
dc
2003
We give a new method to compute the centralizer of an element
in Artin braid groups and, more generally, in Garside groups. This
method, together with the solution of the conjugacy problem given
by the authors in [9] Franco, N. and Gonzalez-Meneses, J.: Conjugacy problem for braid groups and Garside groups, to appear in Journal of Algebra. Available at http://arxiv.org/math.GT/0112310, are two main steps for solving conjugacy systems, thus breaking recently discovered cryptosystems based in braid groups [2] Anshel, I., Anshel, M. and Goldfeld, D.: An algebraic method for public-key cryptography. Math. Res. Lett. 6 (1999), no. 3-4, 287–291. We also present the result of our computations, where we notice that our algorithm yields surprisingly small generating sets for the centralizers.
Gonçalves Soares Franco, N.M. y González-Meneses López, J. (2003). Computation of centralizers in braid groups and Garside groups. Revista Matemática Iberoamericana, 19, 367-384.
0213-2230
2235-0616
http://hdl.handle.net/11441/41158
10.4171/RMI/352
https://idus.us.es/xmlui/handle/11441/41158
Braid group
Garside group
centralizer
cryptography
Computation of centralizers in braid groups and Garside groups
oai:idus.us.es:11441/477112024-02-13T22:14:14Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
1992
Pérez Jiménez, A.d.J. (1992). Matematicas experimentales. Suma. Revista sobre el Aprendizaje y la Enseñanza de las Matemáticas, 11-12, 27-41.
1130-488X
http://hdl.handle.net/11441/47711
https://idus.us.es/xmlui/handle/11441/47711
Matematicas experimentales
oai:idus.us.es:11441/1391752024-02-13T09:59:38Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2019-08-20
We introduce tautological systems defined by prehomogeneous actions of reductive algebraic groups. If the complement of the open orbit is a linear free divisor satisfying a certain finiteness condition, we show that these systems underly mixed Hodge modules. A dimensional reduction is considered and gives rise to one-dimensional differential systems generalizing the quantum differential equation of projective spaces.
Narváez Macarro, L. y Sevenheck, C. (2019). Tautological systems and free divisors. Advances in Mathematics, 352, 372-405. https://doi.org/10.1016/j.aim.2019.06.007.
0001-8708
https://hdl.handle.net/11441/139175
10.1016/j.aim.2019.06.007
Tautological systems
Mixed Hodge modules
Linear free divisors
Tautological systems and free divisors
oai:idus.us.es:11441/447302024-02-17T16:56:10Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2015
We study integral representations of the Gevrey series solutions of irregular hypergeometric systems. In this paper we consider the case of the systems associated with a one row matrix, for which the integration domains are one dimensional. We prove that any Gevrey series solution along the singular support of the system is the asymptotic expansion of a holomorphic
solution given by a carefully chosen integral representation.
Castro Jiménez, F.J. y Granger, M. (2015). Gevrey Expansions of Hypergeometric Integrals I. International Mathematics Research Notices, 2015 (5), 1338-1370.
1073-7928
1687-0247
http://hdl.handle.net/11441/44730
10.1093/imrn/rnt246
https://idus.us.es/xmlui/handle/11441/44730
Gevrey expansions of hypergeometric integrals I
oai:idus.us.es:11441/1391692024-02-17T16:41:56Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2008-04-14
In this paper we survey the role of D-module theory in the comparison between logarithmic and meromorphic de Rham complexes of integrable logarithmic connections with respect to free divisors, and we present some new linearity conditions on the Jacobian ideal which arise in this setting.
Narváez Macarro, L. (2008). Linearity conditions on the Jacobian ideal and logarithmic--meromorphic comparison for free divisors. https://doi.org/10.48550/arXiv.0804.2219.
https://hdl.handle.net/11441/139169
10.48550/arXiv.0804.2219
Free divisor
Jacobian ideal
logarithmic forms
D-module
Bernstein polynomial
Linearity conditions on the Jacobian ideal and logarithmic--meromorphic comparison for free divisors
oai:idus.us.es:11441/462472024-02-13T20:11:20Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2002-10
We find explicit free resolutions for the D-modules Dfs and D[s]fs/D[s]f
s+1, where f is a reduced equation of a locally quasi-homogeneous free divisor. These results are based on the fact that every locally quasi-homogeneous free divisor is Koszul free, which is also proved in this paper.
Calderón Moreno, F.J. y Narváez Macarro, L. (2002). The module Dfs for locally quasi-homogeneous free divisors. Compositio Mathematica, 134 (1), 59-74.
0010-437X
1570-5846
http://hdl.handle.net/11441/46247
10.1023/A:1020228824102
https://idus.us.es/xmlui/handle/11441/46247
Free divisor
De Rham complex
D-module
Locally quasi-homogeneous
Koszul complex
Spencer complex
Ideal of linear type
The module Dfs for locally quasi-homogeneous free divisors
oai:idus.us.es:11441/1391152024-02-14T20:04:49Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2020-02-10
We prove that the space of Gevrey solutions of an A–hypergeometric system along a coordinate subspace is contained in a space of formal Nilsson solutions. Moreover, under some additional condition, both spaces are equal. In the process we prove some other results about formal Nilsson solutions.
Fernández Fernández, M.C. (2020). Gevrey and formal Nilsson solutions of A-hypergeometric systems. Journal of Pure and Applied Algebra, 224 (8), 106350. https://doi.org/10.1016/j.jpaa.2020.106350.
0022-4049
1873-1376
https://hdl.handle.net/11441/139115
10.1016/j.jpaa.2020.106350
A–hypergeometric system
D–module
Gevrey series
Formal Nilsson series
Initial ideals
Gevrey and formal Nilsson solutions of A-hypergeometric systems
oai:idus.us.es:11441/420002018-02-26T07:53:38Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2012
We prove some improvements of the classical Weil bound for one
variable additive and multiplicative character sums associated to a polynomial over a finite field k = Fq for two classes of polynomials which are invariant under a large abelian group of automorphisms of the affine line A1
k: those invariant under translation by elements of k and those invariant under homotheties with ratios in a large subgroup of the multiplicative group of k. In both cases, we are able to improve the bound by a factor of √q over an extension.f k of cardinality sufficiently large compared to the degree of f.
Rojas León, A. (2012). Estimates for exponential sums with a large automorphism group. Contemporary Mathematics, 566, 43-61.
0271-4132
http://hdl.handle.net/11441/42000
10.1090/conm/566/11214
https://idus.us.es/xmlui/handle/11441/42000
Estimates for exponential sums with a large automorphism group
oai:idus.us.es:11441/418992024-02-14T14:01:08Zcom_11441_10883com_11441_10802com_11441_10690com_11441_10803col_11441_10884col_11441_10804
00925njm 22002777a 4500
dc
2004
In this paper we determine the representation type of some algebras of infinite matrices continuously controlled at infinity by a compact metrizable space. We explicitly classify their finitely presented modules in the finite and tame cases. The algebra of row-column-finite (or locally finite) matrices over an arbitrary field is one of the algebras considered in this paper, its representation type is shown to be finite.
Muro Jiménez, F. (2004). Representation theory of some infinite-dimensional algebras arising in continuously controlled algebra and topology. K-theory, 33 (1), 23-65.
0920-3036
http://hdl.handle.net/11441/41899
10.1007/s10977-004-1837-4
https://idus.us.es/xmlui/handle/11441/41899
Representation theory of some infinite-dimensional algebras arising in continuously controlled algebra and topology
oai:idus.us.es:11441/1548222024-02-07T12:09:34Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2023-12-07
The SU(3) tensor multiplicities are piecewise polynomial of degree 1 in their labels. The pieces are the chambers of a complex of cones. We describe in detail this chamber complex and determine the group of all linear symmetries (of order 144) for these tensor multiplicities. We represent the cells by diagrams showing clearly the inclusions as well as the actions of the group of symmetries and of its remarkable subgroups.
Briand, E., Rosas Celis, M.H. y Trandafir, S. (2023). All linear symmetries of the SU(3) tensor multiplicities. Journal of Physics A: Mathematical and Theoretical, 57 (1), 015205-1. https://doi.org/10.1088/1751-8121/ad0dc7.
1751-8113
1751-8121
https://hdl.handle.net/11441/154822
10.1088/1751-8121/ad0dc7
All linear symmetries of the SU(3) tensor multiplicities
oai:idus.us.es:11441/422712016-11-29T12:18:29Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2007
In this paper a relation between iterated cyclings and iterated powers of elements in a Garside group is shown. This yields a characterization of elements in a Garside group having a rigid power, where ‘rigid’ means that the left normal form changes only in the obvious way under cycling and decycling. It is also shown that, given X in a Garside group, if some power X
m is conjugate to a rigid element, then m can be bounded above by ||∆||3. In the particular case of braid groups {Bn, n ∈ N}, this implies that a pseudo-Anosov braid has a small power whose ultra summit set consists of rigid
elements. This solves one of the problems in the way of a polynomial solution to the conjugacy decision problem (CDP) and the conjugacy search problem (CSP) in braid groups. In addition to proving the rigidity theorem, it will be shown how this paper fits into the authors’ program for finding a polynomial algorithm to the CDP/CSP, and what remains to be done.
Birman, J.S., Gebhardt, V. y González-Meneses López, J. (2007). Conjugacy in Garside groups I: cyclings, powers, and rigidity. Groups, Geometry, and Dynamics, 1 (3), 221-279.
1661-7207
1661-7215
http://hdl.handle.net/11441/42271
http://dx.doi.org/10.4171/GGD/12
https://idus.us.es/xmlui/handle/11441/42271
Garside groups
conjugacy problem
ultra summit set
rigidity
stable ultra summit set
Conjugacy in Garside groups I: Cyclings, powers, and rigidity
oai:idus.us.es:11441/703042024-02-14T19:06:36Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2008
Dans cet article, nous proposons une nouvelle méthode pour démontrer la bijectivité de la correspondance de Howe pour les paires duales du type (GLn, GLm) sur un corps F localement compact non archimédien. La preuve est basée sur une étude soigneuse de la filtration de Kudla ainsi que sur les résultats de [A. MÍNGUEZ, Sur l’irréductibilité d’une induite parabolique, prépublication à paraître dans J. reine angew. Math.] à propos de l’irréductibilité d’une représentation induite parabolique. Elle est valable pour F de caractéristique quelconque et nous permet d’expliciter la bijection en termes des paramètres de Langlands. Elle généralise donc les résultats de [T. WATANABE, The local theta correspondence of irreducible type 2 dual reductive pairs, Tohoku Math. J. 47 (1995), 521–540] et répond totalement aux questions étudiées dans [G. MUIC, Howe correspondence for discrete series representations ; the case of (Sp(n), O(V )), J. reine angew. Math. 567 (2004), 99-150] et [G. MUIC, Theta lifts of tempered representations for dual pairs (Sp(2n), O(V )), à paraître dans Canad. J. Math] pour les paires duales de type II.
Mínguez Espallargas, A. (2008). Correspondance de Howe explicite: paires duales de type II. Annales Scientifiques de l'École Normale Supérieure, 41 (5), 717-741.
0012-9593
https://hdl.handle.net/11441/70304
10.24033/asens.2080
Representation theory
Correspondance de Howe explicite: paires duales de type II
oai:idus.us.es:11441/491932024-02-14T11:44:54Zcom_11441_10978com_11441_10802com_11441_10690com_11441_10803col_11441_10979col_11441_10804
00925njm 22002777a 4500
dc
2016
In this paper we use an elementary approach by using numerical
semigroups (specifically, those with two generators) to give a formula for the
number of integral points inside a right-angled triangle with rational vertices.
This is the basic case for computing the number of integral points inside a
rational (not necessarily convex) polygon.
Márquez Campos, G., Ramírez Alfonsín, J.L. y Tornero Sánchez, J.M. (2016). Integral points in rational polygons: a numerical semigroup approach. Semigroup Forum, 1-16.
0037-1912
1432-2137
http://hdl.handle.net/11441/49193
10.1007/s00233-016-9820-y
https://idus.us.es/xmlui/handle/11441/49193
Lattice points
Numerical semigroups
Geometry of numbers
Integral points in rational polygons: a numerical semigroup approach
oai:idus.us.es:11441/744612024-02-17T16:24:07Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2018
We give an elementary proof of the nested Artin approximation Theorem for linear equations with algebraic power series coefficients. Moreover, for any Noetherian local subring of the ring of formal power series, we clarify the relationship between this theorem and the problem of the commutation of two operations for ideals: the operation of replacing an ideal by its completion and the operation of replacing an ideal by one of its elimination ideals. In particular we prove that a Grothendieck conjecture about morphisms of analytic/formal algebras and Artin’s question about linear nested approximation problem are equivalent.
Castro Jiménez, F.J., Popescu, D. y Rond, G. (2018). Linear nested Artin approximation theorem for algebraic power series. Manuscripta mathematica, 1-19.
0025-2611
1432-1785
https://hdl.handle.net/11441/74461
10.1007/s00229-018-1025-0
Henselian rings
Algebraic power series rings
Nested Artin approximation property
Linear nested Artin approximation theorem for algebraic power series
oai:idus.us.es:11441/474642024-02-15T07:40:00Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2015-06
It is known that alternative links are pseudoalternating. In 1983 Louis Kauffman conjectured that both classes are identical. In this paper we prove that Kauffman Conjecture holds for those links whose first Betti number is at most 2. However, it is not true in general when this value increases, as we also prove by finding two counterexamples: a link and a knot whose first Betti numbers equal 3 and 4, respectively.
Silvero Casanova, M. (2015). On a conjecture by Kauffman on alternative and pseudoalternating links. Topology and its Applications, 188, 82-90.
0166-8641
1879-3207
http://hdl.handle.net/11441/47464
10.1016/j.topol.2015.03.012
https://idus.us.es/xmlui/handle/11441/47464
Alternative links
Homogeneous links
Pseudoalternating links
On a conjecture by Kauffman on alternative and pseudoalternating links
oai:idus.us.es:11441/1063532024-02-12T21:43:55Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2019-05-31
A Dwork family is a one-parameter monomial deformation of a Fermat hypersurface. In this paper we compute algebraically the invariant part of its Gauss–Manin cohomology under the action of certain subgroup of automorphisms. To achieve that goal we use the algebraic theory of D-modules, especially one-dimensional hypergeometric ones.
Castaño Domínguez, A. (2019). Dwork families and D-modules. Revista Matemática Iberoamericana, 35 (5), 1451-1484.
2235-0616
https://hdl.handle.net/11441/106353
10.4171/rmi/1088
D-modules, Gauss–Manin systems, Dwork families, hypergeometric D-modules
Dwork families and D-modules
oai:idus.us.es:11441/1442162023-04-14T09:42:02Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804oai:idus.us.es:11441/431052024-02-17T16:49:23Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2005-03-15
Let k be a perfect field of positive characteristic, k(t)per the perfect closure of k(t)
and A = k[[X1, . . . , Xn]]. We show that for any maximal ideal n of A′ = k(t)per ⊗k A,
the elements in Ac′
n which are annihilated by the “Taylor” Hasse-Schmidt derivations
with respect to the Xi form a coefficient field of Ac′
n
.
Fernández Lebrón, M.M. y Narváez Macarro, L. (2005). Coefficient fields and scalar extension in positive characteristic. Journal of Algebra, 285 (2), 819-834.
0021-8693
1090-266X
http://hdl.handle.net/11441/43105
10.1016/j.jalgebra.2004.11.009
https://idus.us.es/xmlui/handle/11441/43105
Complete local ring
Coefficient field
Hasse-Schmidt derivation
Coefficient fields and scalar extension in positive characteristic
oai:idus.us.es:11441/422912024-02-13T22:27:43Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2014-09-01
We study the Morton-Franks-Williams inequality for closures of simple
braids (also known as positive permutation braids). This allows to prove,
in a simple way, that the set of simple braids is a orthonormal basis for
the inner product of the Hecke algebra of the braid group defined by
K´alm´an, who first obtained this result by using an interesting connection
with Contact Topology. We also introduce a new technique to study the Homflypt polynomial for closures of positive braids, namely resolution trees whose leaves are simple braids. In terms of these simple resolution trees, we characterize closed positive braids for which the Morton-Franks-Williams inequality is strict. In particular, we determine explicitly the positive braid words on three strands whose closures have braid index three.
González-Meneses López, J. y González Manchón, P.M. (2014). Closures of positive braids and the Morton-Franks-Williams inequality. Topology and its Applications, 174 (1), 14-24.
0166-8641
http://hdl.handle.net/11441/42291
http://dx.doi.org/10.1016/j.topol.2014.06.008
https://idus.us.es/xmlui/handle/11441/42291
Positive braid
Morton–Franks–Williams inequality
Homflypt polynomial
Braid index
Closures of positive braids and the Morton-Franks-Williams inequality
oai:idus.us.es:11441/430242024-02-14T11:11:09Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2014
We prove, under mild assumptions, that a Quillen equivalence between symmetric monoidal model categories gives rise to a Quillen equivalence between their model categories of (non-symmetric) operads, and also between model categories of algebras over operads. We also show left properness results on model categories of operads and algebras over operads. As an application, we prove homotopy invariance for (unital) associative operads.
Muro Jiménez, F. (2014). Homotopy theory of non-symmetric operads, II: Change of base category and left properness. Algebraic and Geometric Topology, 14, 229-281.
1472-2747
1472-2739
http://hdl.handle.net/11441/43024
http://dx.doi.org/10.2140/agt.2014.14.229
https://idus.us.es/xmlui/handle/11441/43024
operad
algebra
model category
Quillen equivalence
A–infinity algebra
Homotopy theory of non-symmetric operads, II: Change of base category and left properness
oai:idus.us.es:11441/420412019-04-03T06:09:21Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2011-08-01
We describe the Gevrey series solutions at singular points of the irregular hypergeometric system (GKZ system) associated with an affine plane monomial curve. We also describe the irregularity complex of such a system with respect to its singular support and in particular we prove, using elementary methods, that this irregularity complex is a perverse sheaf as assured by a theorem of Z. Mebkhout.
Fernández Fernández, M.C. y Castro Jiménez, F.J. (2011). Gevrey solutions of irregular hypergeometric systems in two variables. Journal of Algebra, 339 (1), 320-335.
1090-266X
0021-8693
http://hdl.handle.net/11441/42041
10.1016/j.jalgebra.2011.02.045
https://idus.us.es/xmlui/handle/11441/42041
Weyl algebra
Affine monomial curve
Toric ideal
Hypergeometric system
Gevrey series
Irregular D-module
Gevrey solutions of irregular hypergeometric systems in two variables
oai:idus.us.es:11441/531922024-02-13T22:01:55Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2013
Rojas León, A. (2013). Pierre Deligne. La Gaceta de la Real Sociedad Matemática Española, 16 (3), 575-592.
1138-8927
http://hdl.handle.net/11441/53192
Pierre Deligne
oai:idus.us.es:11441/475302024-02-14T09:10:54Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2012-04-15
Benardete, Gutierrez and Nitecki showed an important result which relates the geometrical properties of a braid, as a homeomorphism of the punctured disk, to its algebraic Garside-theoretical properties. Namely, they showed that if a braid sends a standard curve to another standard curve, then the image of this curve after each factor of the left normal form of the braid (with the classical Garside structure) is also standard. We provide a new simple,
geometric proof of the result by Benardete-Gutierrez-Nitecki, which can be easily adapted to the case of the dual Garside structure of braid groups, with the appropriate definition of standard curves in the dual setting. This yields a new algorithm for determining the Nielsen-Thurston type of braids.
Calvez, M. (2012). Dual Garside structure and reducibility of braids. Journal of Algebra, 356 (1), 355-373.
0021-8693
http://hdl.handle.net/11441/47530
10.1016/j.jalgebra.2012.01.022
https://idus.us.es/xmlui/handle/11441/47530
Nielsen-Thurston classification
Dual braids
Dual Garside structure and reducibility of braids
oai:idus.us.es:11441/430662024-02-13T10:02:47Zcom_11441_10893com_11441_10802com_11441_10690com_11441_10803col_11441_10894col_11441_10804
00925njm 22002777a 4500
dc
2019
We study the commutation relations and normal ordering between
families of operators on symmetric functions. These operators can be naturally defined by the operations of multiplication, Kronecker product, and their adjoints. As applications we give a new proof of the skew Littlewood–Richardson rule and prove an identity about the Kronecker product with a skew Schur function.
Briand, E., McNamara, P.R.W., Orellana, R.C. y Rosas Celis, M.H. (2019). Commutation and normal ordering for operators on symmetric functions. Seminaire Lotharingien de Combinatoire, 80, B80d-1.
http://hdl.handle.net/11441/43066
https://idus.us.es/xmlui/handle/11441/43066
Commutation and normal ordering for operators on symmetric functions
oai:idus.us.es:11441/419552024-02-13T08:47:32Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2010-08
We find a tight relationship between the torsion subgroup and the image of the mod 2 Galois representation associated to an elliptic curve defined over the rationals. This is shown using some characterizations for the squareness of the discriminant of the elliptic curve.
García Selfa, I., González Jiménez, E. y Tornero Sánchez, J.M. (2010). Galois Theory, discriminants and torsion subgroups of elliptic curves. Journal of Pure and Applied Algebra, 214 (8), 1340-1346.
0022-4049
http://hdl.handle.net/11441/41955
http://dx.doi.org/10.1016/j.jpaa.2009.11.001
https://idus.us.es/xmlui/handle/11441/41955
Elliptic curves
Cubic equations
Torsion subgroup
Galois theory
Galois Theory, discriminants and torsion subgroups of elliptic curves
oai:idus.us.es:11441/418742024-02-13T21:56:30Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2008-11
We show that the symmetric track groups Sym(n), which are extensions
of the symmetric groups Sym(n) associated to the second Stiefel-Whitney
class, act as crossed modules on the secondary homotopy groups of a pointed
space.
Baues, H.J. y Muro Jiménez, F. (2008). The symmetric action on secondary homotopy groups. Bulletin of the Belgian Mathematical Society Simon Stevin, 15 (4), 733-768.
1370-1444
http://hdl.handle.net/11441/41874
https://idus.us.es/xmlui/handle/11441/41874
secondary homotopy groups
crossed module
square group
cup-one product
The symmetric action on secondary homotopy groups
oai:idus.us.es:11441/419342024-02-14T13:43:32Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2009-12
This paper extends previous results of the authors, concerning the behaviour of the equimultiple locus of algebroid surfaces under blowing–up, to arbitrary characteristic.
Piedra Sánchez, R. y Tornero Sánchez, J.M. (2009). Equimultiple locus of embedded algebroid surfaces and blowing--up in arbitrary characteristic. Algebra Colloquium, 16 (4), 575-586.
1005-3867
0219-1733
http://hdl.handle.net/11441/41934
http://dx.doi.org/10.1142/S1005386709000546
https://idus.us.es/xmlui/handle/11441/41934
algebroid surfaces
equimultiple locus
resolution of singularities
Equimultiple locus of embedded algebroid surfaces and blowing-up in arbitrary characteristic
oai:idus.us.es:11441/1443912024-02-14T20:07:30Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2022-05-28
In this paper we present a refined version of MacLane's theory of key polynomials, similar to those considered by M. Vaqui\'e and reminiscent of approximate roots of Abhyankar and Moh. Given a simple transcendental extension of valued fields, we associate to it a countable well-ordered set of polynomials called key polynomials. We define limit key polynomials and give explicit formulae for them. We give an explicit bound on the order type of the set of key polynomials.
Herrera Govantes, F.J., Mahboub, W. y Olalla Acosta, M.Á. (2022). Key polynomials for simple extensions of valued fields. Journal of singularities, 25, 197-267. https://doi.org/10.5427/jsing.2022.25k.
1949-2006
https://hdl.handle.net/11441/144391
10.5427/jsing.2022.25k
Key polynomials for simple extensions of valued fields
oai:idus.us.es:11441/1535592024-02-13T22:06:56Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2020-02-29
Rosas Celis, M.H. y Briand, E. (2020). Schur generating functions and the asymptotics of structural constants from combinatorial representation theory. Oberwolfach Reports, 17 (1), 548-551. https://doi.org/10.4171/OWR/2020/9.
https://hdl.handle.net/11441/153559
10.4171/OWR/2020/9
Schur generating functions and the asymptotics of structural constants from combinatorial representation theory
oai:idus.us.es:11441/420042024-02-14T08:49:58Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2013-01
Using Weil descent, we give bounds for the number of rational points on two families of curves over finite fields with a large abelian group of automorphisms: Artin–Schreier curves of the form yq−y=f(x) with f∈Fqr[x], on which the additive group Fq acts, and Kummer curves of the form , which have an action of the multiplicative group . In both cases we can remove a factor from the Weil bound when q is sufficiently large.
Rojas León, A. (2013). On the number of rational points on curves over finite fields with many automorphisms. Finite Fields and Their Applications, 19 (1), 1-15.
1071-5797
1090-2465
http://hdl.handle.net/11441/42004
10.1016/j.ffa.2012.11.001
https://idus.us.es/xmlui/handle/11441/42004
Point counting
Weil bound
ℓ-adic cohomology
Weil descent
On the number of rational points on curves over finite fields with many automorphisms
oai:idus.us.es:11441/474092024-02-12T22:16:12Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2011-05-15
Let us consider an abelian variety defined over Qℓ with good supersingular
reduction. In this paper we give explicit conditions that ensure that the action of the wild inertia group on the ℓ-torsion points of the variety is trivial. Furthermore we give a family of curves of genus 2 such that their Jacobian surfaces have good supersingular reduction and satisfy these conditions. We address this question by means of a detailed study of the formal group law attached to abelian varieties.
Arias de Reyna Domínguez, S. (2011). Formal groups, supersingular abelian varieties and tame ramification. Journal of Algebra, 334 (1), 84-100.
0021-8693
http://hdl.handle.net/11441/47409
10.1016/j.jalgebra.2011.03.010
https://idus.us.es/xmlui/handle/11441/47409
Tame ramification
Formal group
Supersingular abelian variet
Formal groups, supersingular abelian varieties and tame ramification
oai:idus.us.es:11441/419522024-02-14T09:23:08Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2002-09
It is a classical result (apparently due to Tate) that all elliptic curves with a torsion point of order n (4 ≤ n ≤ 10, or n = 12) lie in a oneparameter family. However, this fact does not appear to have been used ever for computing the torsion of an elliptic curve. We present here a extremely down–to–earth algorithm using the existence of such a family.
García Selfa, I., Olalla Acosta, M.Á. y Tornero Sánchez, J.M. (2002). Computing the rational torsion of an elliptic curve using Tate normal form. Journal of Number Theory, 96 (1), 76-88.
1096-1658
http://hdl.handle.net/11441/41952
http://dx.doi.org/10.1006/jnth.2002.2780
https://idus.us.es/xmlui/handle/11441/41952
elliptic curves
rational points
Computing the rational torsion of an elliptic curve using Tate normal form
oai:idus.us.es:11441/419042024-02-12T21:33:20Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2011
The primary algebraic model of a ring spectrum R is the ring π∗R of homotopy groups. We introduce the secondary model π∗,∗R which has the
structure of a secondary analogue of a ring. The homology of π∗,∗R is π∗R
and triple Massey products in π∗,∗R coincide with Toda brackets in π∗R. We
also describe the secondary model of a commutative ring spectrum Q from
which we derive the cup-one square operation in π∗Q. As an application we
obtain for each ring spectrum R new derivations of the ring π∗R.
Baues, H.J. y Muro Jiménez, F. (2011). The algebra of secondary homotopy operations in ring spectra. Proceedings of the London Mathematical Society, 102 (4), 637-696.
0024-6115
1460-244X
http://hdl.handle.net/11441/41904
10.1112/plms/pdq034
https://idus.us.es/xmlui/handle/11441/41904
Ring spectrum
homotopy groups
secondary homotopy groups
Toda bracket
Massey product
cup-one product
Shukla cohomology
Mac Lane cohomology
permutative category
quadratic pair module
The algebra of secondary homotopy operations in ring spectra
oai:idus.us.es:11441/477132024-02-14T11:44:57Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
1997-06
Pérez Jiménez, A.d.J. (1997). Semblanza del profesor don Gonzalo Sánchez Vázquez. Suma. Revista sobre el Aprendizaje y la Enseñanza de las Matemáticas, 25, 7-14.
1130-488X
http://hdl.handle.net/11441/47713
https://idus.us.es/xmlui/handle/11441/47713
Semblanza del profesor don Gonzalo Sánchez Vázquez
oai:idus.us.es:11441/422602024-02-14T19:19:58Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2008-09-06
The cycling operation is a special kind of conjugation that can be applied to elements in Artin’s braid groups, in order to reduce their length. It is a key ingredient of the usual solutions to the conjugacy problem in braid groups. In their seminal paper on braid-cryptography, Ko, Lee et al. proposed the cycling problem as a hard problem in braid groups that could be interesting for cryptography. In this paper we give a polynomial solution to that problem,
mainly by showing that cycling is surjective, and using a result by Maffre which shows that pre-images under cycling can be computed fast. This result also holds in every Artin-Tits group of spherical type. On the other hand, the conjugacy search problem in braid groups is usually solved by
computing some finite sets called (left) ultra summit sets (left-USS), using left normal forms of braids. But one can equally use right normal forms and compute right-USS’s. Hard instances of the conjugacy search problem correspond to elements having big (left and right) USS’s. One may think that even if some element has a big left-USS, it could possibly have a small right-USS. We show that this is not the case in the important particular case of rigid braids. More precisely, we show that the left-USS and the right-USS of a given rigid braid determine isomorphic graphs, with the arrows reversed, the isomorphism being defined using iterated cycling. We conjecture that the same is true for every element, not necessarily rigid, in braid groups and Artin-Tits groups of spherical type.
González-Meneses López, J. y Gebhardt, V. (2008). On the cycling operation in braid groups. Discrete Applied Mathematics, 156 (16), 3072-3090.
0166-218X
http://hdl.handle.net/11441/42260
10.1016/j.dam.2008.01.023
https://idus.us.es/xmlui/handle/11441/42260
Braid groups
Garside groups
Conjugacy problem
Conjugacy search problem
Cycling
Ultra summit set
Braid-based cryptography
On the cycling operation in braid groups
oai:idus.us.es:11441/597402017-05-15T06:56:23Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2017
We define a K-theory for pointed right derivators and show that it agrees with Waldhausen K-theory in the case where the derivator arises from a good Waldhausen category. This K-theory is not invariant under general equivalences of derivators, but only under a stronger notion of equivalence that is defined by considering a simplicial enrichment of the category of derivators. We show that derivator K-theory, as originally defined, is the best approximation to Waldhausen K-theory by a functor that is invariant under equivalences of derivators.
Muro Jiménez, F. y Raptis, G. (2017). K-theory of derivators revisited. Annals of K-theory, 2 (2), 303-340.
2379-1683
2379-1691
http://hdl.handle.net/11441/59740
10.2140/akt.2017.2.303
K-theory
Derivator
K-theory of derivators revisited
oai:idus.us.es:11441/476152016-11-29T12:18:30Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2013
Let F be a non-Archimedean locally compact field of residue characteristic p, let D be a finite dimensional central division F-algebra and let R be an algebraically closed field of characteristic different from p. We define banal irreducible R-representations of the group G = GLm(D). This notion involves a condition on the cuspidal support of the representation depending on the
characteristic of R. When this characteristic is banal with respect to G, in particular when R is the field of complex numbers, any irreducible R-representation of G is banal. In this article, we give a classification of all banal irreducible R-representations of G in terms of certain multisegments,
called banal. When R is the field of complex numbers, our method provides a new proof, entirely local, of Tadi´c’s classification of irreducible complex smooth representations of G.
Mínguez Espallargas, A. (2013). Représentations banales de GLm(D). Compositio Mathematica, 149, 679-704.
0010-437X
1570-5846
http://hdl.handle.net/11441/47615
10.1112/S0010437X12000590
https://idus.us.es/xmlui/handle/11441/47615
Representations of p-adic groups
Modular representation
Multisegment
Banal representation
Représentations banales de GLm(D)
oai:idus.us.es:11441/467862024-02-17T17:11:36Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2003
We consider categories of generalized perverse sheaves, with relaxed constructibility conditions, by means of the process of gluing t-structures and we exhibit explicit abelian categories defined in terms of standard sheaves categories which are equivalent to the former ones. In particular, we are able to realize perverse sheaves categories as non full abelian subcategories of the usual bounded complexes of sheaves categories. Our
methods use induction on perversities. In this paper, we restrict ourselves to the twostrata case, but our results extend to the general case.
Gudiel Rodríguez, F. y Narváez Macarro, L. (2003). Explicit models for perverse sheaves. Revista Matemática Iberoamericana, 19 (2), 425-454.
0213-2230
http://hdl.handle.net/11441/46786
https://idus.us.es/xmlui/handle/11441/46786
Perverse sheaf
Derived category
T-structure
Stratified space
Abelian category
Explicit models for perverse sheaves
oai:idus.us.es:11441/236012024-02-13T08:49:17Zcom_11441_10893com_11441_10802com_11441_10690com_11441_10803col_11441_10894col_11441_10804
00925njm 22002777a 4500
dc
2013-11
The redundancy allocation problem is formulated minimizing the design cost for a series-parallel system with multiple component choices while ensuring a given system reliability level. The obtained model is a nonlinear integer programming problem with a nonlinear, nonseparable constraint. We propose a method based on the construction of a test set of an integer linear problem, which allows us to obtain an exact solution of the problem. It is compared to other approaches in the literature and standard nonlinear solvers.
Gago-Vargas, J., Hartillo I., Puerto, J., Ucha, J.M., (2013) Exact cost minimization of a series-parallel reliable system with multiple component choices using an algebraic method. Computers & Operations Research. Vol. 40. Núm. 11. p. 2752-2759.
0305-0548
http://hdl.handle.net/11441/23601
10.1016/j.cor.2013.05.019
https://idus.us.es/xmlui/handle/11441/23601
Reliability
Integer programming
Test set
Exact cost minimization of a series-parallel reliable system with multiple component choices using an algebraic method
oai:idus.us.es:11441/431172024-02-14T19:10:31Zcom_11441_10893com_11441_10802com_11441_10690com_11441_10803col_11441_10894col_11441_10804
00925njm 22002777a 4500
dc
2005
There are recent cryptographic protocols that are based on Multiple
Simultaneous Conjugacy Problems in braid groups. We improve an algorithm,
due to Sang Jin Lee and Eonkyung Lee, to solve these problems, by
applying a method developed by the author and Nuno Franco, originally
intended to solve the Conjugacy Search Problem in braid groups.
González-Meneses López, J. (2005). Improving an algorithm to solve multiple simultaneous conjugacy problems in braid groups. Contemporary Mathematics, 372, 35-42.
0271-4132
http://hdl.handle.net/11441/43117
10.1090/conm/372/06872
https://idus.us.es/xmlui/handle/11441/43117
Improving an algorithm to solve multiple simultaneous conjugacy problems in braid groups
oai:idus.us.es:11441/1391102024-02-14T13:33:24Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2018-09-22
The minimal standardizer of a curve system on a punctured disk is the minimal positive braid that transforms it into a system formed only by round curves. We give an algorithm to compute it in a geometrical way. Then, we generalize this problem algebraically to parabolic subgroups of Artin–Tits groups of spherical type and we show that, to compute the minimal standardizer of a parabolic subgroup, it suffices to compute the pn-normal form of a particular central element.
Cumplido Cabello, M. (2018). On the minimal positive standardizer of a parabolic subgroup of an Artin–Tits group. Journal of algebraic combinatorics, 49 (3), 337-359. https://doi.org/10.1007/s10801-018-0837-z.
0925-9899
0925-9899
https://hdl.handle.net/11441/139110
10.1007/s10801-018-0837-z
Braid groups
Curve complex
Artin groups
Parabolic subgroups
Garside theory
On the minimal positive standardizer of a parabolic subgroup of an Artin–Tits group
oai:idus.us.es:11441/420232024-02-14T08:51:39Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2013-08
For K and L two l-adic perverse sheaves on the one-dimensional torus Gm,k¯ over the algebraic closure of a finite field, we show that the local
monodromies of their convolution K ∗ L at its points of non-smoothness is
completely determined by the local monodromies of K and L. We define local
convolution bi-exact functors ρ(u) (s,t) for every s, t, u ∈ P 1 k¯that map continuous l-adic representations of the inertia groups at s and t to a representation of the inertia group at u, and show that the local monodromy of K ∗ L at u is the direct sum of the ρ(u) (s,t) applied to the local monodromies of K and L. This generalizes a previous result of N. Katz for the case where K and L are smooth, tame at 0 and totally wild at infinity.
Rojas León, A. (2013). Local convolution of l-adic sheaves on the torus. Mathematische Zeitschrift, 274 (3), 1211-1230.
0025-5874
1432-1823
http://hdl.handle.net/11441/42023
http://dx.doi.org/10.1007/s00209-012-1113-x
https://idus.us.es/xmlui/handle/11441/42023
Convolution ℓ-adic cohomology Monodromy Perverse sheaves
Local convolution of l-adic sheaves on the torus
oai:idus.us.es:11441/418732024-02-14T20:08:11Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2007-12-01
We give a small functorial algebraic model for the 2-stage Postnikov
section of the K-theory spectrum of a Waldhausen category and use our
presentation to describe the multiplicative structure with respect to biexact
functors.
Muro Jiménez, F. y Tonks, A. (2007). The 1-type of a Waldhausen K-theory spectrum. Advances in Mathematics, 216 (1), 178-211.
0001-8708
1090-2082
http://hdl.handle.net/11441/41873
10.1016/j.aim.2007.05.008
https://idus.us.es/xmlui/handle/11441/41873
K-theory
Waldhausen category
Postnikov invariant
Stable quadratic module
Crossed complex
Categorical group
The 1-type of a Waldhausen K-theory spectrum
oai:idus.us.es:11441/475792024-02-17T16:21:35Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2014-06
In this article we present a combinatorial treatment of normal flatness in analytic spaces, using the idea of equimultiple standard bases. We will prove, using purely combinatorial methods, a characterization theorem for normal flatness. This will lead us to a new proof of a classical theorem on normal flatness, which can be stated by saying that normal flatness at a point along a smooth subspace is equivalent to the Hilbert function being locally constant. Though these topics belong to classical analytic geometry, we believe that this approach is valuable, since it replaces extremely general algebraic theorems by combinatorial objects, obtaining new results and striking the combinatorial nature of the classical (and basic) ideas in the resolution of singularities.
Soto Prieto, M.J. y Tornero Sánchez, J.M. (2014). Some combinatorial remarks on normal flatness in analytic spaces. Taiwanese Journal of Mathematics, 18 (3), 943-971.
1027-5487
2224-6851
http://hdl.handle.net/11441/47579
10.11650/tjm.18.2014.3306
https://idus.us.es/xmlui/handle/11441/47579
Analytic spaces
Resolution of singularities
Normal flatness
Some combinatorial remarks on normal flatness in analytic spaces
oai:idus.us.es:11441/838572024-02-17T16:24:42Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2018-06
We prove that the hypothetical extreme Khovanov cohomology of a link is the cohomology of the independence simplicial complex of its Lando graph. We also provide a family of knots having as many non-trivial extreme Khovanov cohomology modules as desired, that is, examples of H-thick knots which are as far of being H-thin as desired.
González-Meneses López, J., González Manchón, P.M. y Silvero Casanova, M. (2018). A geometric description of the extreme Khovanov cohomology. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 148 (3), 541-557.
0308-2105
1473-7124
https://hdl.handle.net/11441/83857
10.1017/S0308210517000300
Knots and links
Khovanov cohomology
Independence complex
H-thick knots
Lando graph
A geometric description of the extreme Khovanov cohomology
oai:idus.us.es:11441/545432024-02-14T11:15:11Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2015
These are Lecture Notes of a course given by the author at the School Winter Braids, held at the Université de Pau et des Pays de L’Adour (France), on February 2015. It is explained how mapping class groups, and in particular braid groups, act on some interesting geometric spaces like the hyperbolic plane and the complex of curves, and how this allows to obtain some algebraic properties of the groups. A proof of the hyperbolicity
of the graph of curves, following Hensel-Przytycki-Webb, is given.
González-Meneses López, J. (2015). Geometric approaches to braid groups and mapping class groups. Winter Braids Lecture Notes, 2, 1-25.
2426-0312
http://hdl.handle.net/11441/54543
10.5802/wbln.9
Geometric approaches to braid groups and mapping class groups
oai:idus.us.es:11441/420312024-02-14T20:32:59Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2007-06-15
Let K → L be an algebraic field extension and ν a valuation of K. The purpose of this paper is to describe the totality of extensions {ν′} of ν to L using a refined version of MacLane’s key polynomials. In the basic case when L is a finite separable extension and rk ν = 1, we give an explicit description of the limit key polynomials (which can be viewed as a generalization of the Artin–Schreier polynomials). We also give a realistic upper bound on the order type of the set of key polynomials. Namely, we show that if char K = 0 then the set of key polynomials has order type at most N, while in the case char K = p > 0 this order type is bounded above by
logp n + 1 ω, where n = [L : K]. Our results provide a new point of view of the
the well known formula Ps j=1 ejfjdj = n and the notion of defect.
Herrera Govantes, F.J., Olalla Acosta, M.Á. y Spivakovsky. Mark, (2007). Valuations in algebraic field extensions. Journal of Algebra, 312 (2), 1033-1074.
1090-266X
0021-8693
http://hdl.handle.net/11441/42031
10.1016/j.jalgebra.2007.02.022
https://idus.us.es/xmlui/handle/11441/42031
valuation
algebraic extension
key polynomial
Newton polygon
Valuations in algebraic field extensions
oai:idus.us.es:11441/422632024-02-13T09:32:28Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2013-01
We present an algorithm to generate positive braids of a given length as words in Artin generators with a uniform probability. The complexity of this algorithm is polynomial in the number of strands and in the length of the generated braids. As a byproduct, we describe a finite state automaton accepting the language of lexicographically minimal representatives of positive braids that has the minimal possible number of states, and we prove that its number of states is exponential in the number of strands.
Gebhardt, V. y González-Meneses López, J. (2013). Generating random braids. Journal of Combinatorial Theory, Series A, 120 (1), 111-128.
0097-3165
1096-0899
http://hdl.handle.net/11441/42263
10.1016/j.jcta.2012.07.003
https://idus.us.es/xmlui/handle/11441/42263
Random braids
Uniform random generator
Lexicographically minimal representatives
Regular language
Forbidden prefixes
Finite state automata
Generating random braids
oai:idus.us.es:11441/475182024-02-15T07:39:56Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2014
We prove the existence of an algorithm that solves the reducibility problem in braid groups and runs in quadratic time with respect to the braid length for any fixed braid index.
Calvez, M. (2014). Fast Nielsen-Thurston classification of braids. Algebraic and Geometric Topology, 14 (3), 1745-1758.
1472-2747
1472-2739
http://hdl.handle.net/11441/47518
10.2140/agt.2014.14.1745
https://idus.us.es/xmlui/handle/11441/47518
Braid groups
Nielsen-Thurston classification
Fast Nielsen-Thurston classification of braids
oai:idus.us.es:11441/1444602024-03-01T10:12:06Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2023-02-01
We provide an effective version of Katz’ criterion for finiteness of the monodromy group of
a lisse, pure of weight zero, -adic sheaf on a normal variety over a finite field, depending
on the numerical complexity of the sheaf.
Rojas Leon, A. (2023). An Effective Criterion for Finite Monodromy of ℓ-Adic Sheaves. Vietnam Journal of Mathematics. https://doi.org/10.1007/s10013-022-00603-1.
2305-221X
2305-2228
https://hdl.handle.net/11441/144460
10.1007/s10013-022-00603-1
l-adic cohomology
Monodromy
An Effective Criterion for Finite Monodromy of ℓ-Adic Sheaves
oai:idus.us.es:11441/430192024-02-14T13:37:28Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2005
The concept of a triangulated homotopy category can be canonically lifted to
the level of a groupoid-enriched category. This way two natural axioms on track triangles replace the four somewhat obscure axioms of a triangulated category.
http://hdl.handle.net/11441/43019
https://idus.us.es/xmlui/handle/11441/43019
triangulated categories
groupoid-enriched categories
The characteristic cohomology class of a triangulated category
oai:idus.us.es:11441/852712024-02-14T19:18:04Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2019-02-06
We describe the role of the Schur multiplier in the structure of the p-torsion of
discrete groups. More concretely, we show how the knowledge of H2G allows us to approximate many groups by colimits of copies of p-groups. Our examples include interesting families of noncommutative infinite groups, including Burnside groups, certain solvable groups and branch groups. We also provide a counterexample for a conjecture of Emmanuel Farjoun.
Flores Díaz, R.J. y Muro Jiménez, F. (2019). Torsion homology and cellular approximation. Algebraic and Geometric Topology, 19, 457-476.
1472-2747
1472-2739
https://hdl.handle.net/11441/85271
10.2140/agt.2019.19.457
Homology
Approximation
Torsion homology and cellular approximation
oai:idus.us.es:11441/430272024-02-14T20:15:46Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2015
We construct a model structure on the category of small categories
enriched over a combinatorial closed symmetric monoidal model category satisfying the monoid axiom. Weak equivalences are Dwyer–Kan equivalences, i.e. enriched functors which induce weak equivalences on morphism objects and equivalences of ordinary categories when we take sets of connected components on morphism objects.
Muro Jiménez, F. (2015). Dwyer-Kan homotopy theory of enriched categories. Journal of Topology, 8 (2), 377-413.
1753-8416
1753-8424
http://hdl.handle.net/11441/43027
http://dx.doi.org/10.1112/jtopol/jtu029
https://idus.us.es/xmlui/handle/11441/43027
enriched category
model category
Dwyer-Kan homotopy theory of enriched categories
oai:idus.us.es:11441/419672019-04-03T06:09:24Zcom_11441_10893com_11441_10802com_11441_10690com_11441_10803col_11441_10894col_11441_10804
00925njm 22002777a 4500
dc
2004
In this paper we show that the singular braid monoid of an orientable
surface can be embedded in a group. The proof is purely topological,
making no use of the monoid presentation.
Díaz Cantos, J., González-Meneses López, J. y Tornero Sánchez, J.M. (2004). On the singular braid monoid of an orientable surface. Proceedings of the American Mathematical Society, 132 (10), 2867-2873.
0002-9939
1088-6826
http://hdl.handle.net/11441/41967
10.1090/S0002-9939-04-07307-1
https://idus.us.es/xmlui/handle/11441/41967
Singular braids
On the singular braid monoid of an orientable surface
oai:idus.us.es:11441/418752024-02-13T20:08:31Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2015
We extend Deligne’s notion of determinant functor to Waldhausen categories
and (strongly) triangulated categories. We construct explicit universal determinant functors in each case, whose target is an algebraic model for the 1-type of the corresponding K-theory spectrum. As applications, we answer open questions by Maltsiniotis and Neeman on the K-theory of (strongly) triangulated categories and a question of Grothendieck to Knudsen on determinant functors. We also prove additivity theorems for low-dimensional K-theory of (strongly) triangulated categories and obtain generators and (some) relations for various K1-groups. This is achieved
via a unified theory of determinant functors which can be applied in further contexts, such as derivators.
Muro Jiménez, F., Tonks, A. y Witte, M. (2015). On determinant functors and K-theory. Publicacions matemàtiques, 59 (1), 137-233.
0214-1493
2014-4350
http://hdl.handle.net/11441/41875
10.5565/PUBLMAT_59115_07
https://idus.us.es/xmlui/handle/11441/41875
Determinant functor
K-theory
exact category
Waldhausen category
triangulated category
Grothendieck derivator
On determinant functors and K-theory
oai:idus.us.es:11441/419592024-02-14T19:25:42Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2013-06
We study the solutions of the Rosenberg–Markoff equation ax2 + by2 + cz2 = dxyz (a generalization of the well–known Markoff equation). We specifically focus on looking for solutions in arithmetic progression that lie in the ring of integers of a number field. With the help of previous work by Alvanos and Poulakis, we give a complete decision algorithm, which allows us to prove finiteness results concerning these particular solutions. Finally, some extensive computations are presented regarding two particular cases: the generalized Markoff equation x 2 +y 2 +z 2 = dxyz over quadratic fields and
the classic Markoff equation x 2 + y 2 + z 2 = 3xyz over an arbitrary number
field.
González Jiménez, E. y Tornero Sánchez, J.M. (2013). Markoff-Rosenberger triples in arithmetic progression. Journal of Symbolic Computation, 53, 53-63.
0747-7171
http://hdl.handle.net/11441/41959
10.1016/j.jsc.2012.11.003
https://idus.us.es/xmlui/handle/11441/41959
Markoff equation
arithmetic progression
Markoff-Rosenberger triples in arithmetic progression
oai:idus.us.es:11441/418792024-02-14T19:40:40Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2008-10
We construct a smash product operation on secondary homotopy
groups yielding the structure of a lax symmetric monoidal functor. Applications
on cup-one products, Toda brackets and Whitehead products are considered.
Bauer, H.J. y Muro Jiménez, F. (2008). Smash products for secondary homotopy groups. Applied Categorical Structures, 16 (5), 551-616.
0927-2852
1572-9095
http://hdl.handle.net/11441/41879
10.1007/s10485-007-9071-X
https://idus.us.es/xmlui/handle/11441/41879
Secondary homotopy group
square group
crossed module
smash product
lax symmetric monoidal functor
Whitehead product
cup-one product
Toda bracket
Smash products for secondary homotopy groups
oai:idus.us.es:11441/419372024-02-14T20:20:20Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2004
The smooth equimultiple locus of embedded algebroid surfaces appears
naturally in many resolution process, both classical and modern.In this paper we explore how it changes by blowing–up.
Piedra Sánchez, R. y Tornero Sánchez, J.M. (2004). Equimultiple locus of embedded algebroid surfaces and blowing-up in characteristic zero. Serdica Mathematical Journal, 30 (2), 195-206.
1310-6600
http://hdl.handle.net/11441/41937
https://idus.us.es/xmlui/handle/11441/41937
Resolution of surface singularities
blowing–up
equimultiple locus
Equimultiple locus of embedded algebroid surfaces and blowing-up in characteristic zero
oai:idus.us.es:11441/416882024-02-13T10:03:25Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2011-04-01
In the late 1930’s Murnaghan discovered the existence of a stabilization phenomenon for the Kronecker product of Schur functions. For n sufficiently large, the values of the Kronecker coefficients appearing in the product of two Schur functions of degree n do not depend on the first part of the indexing partitions, but only on the values of their remaining parts. We compute the exact value of n for which all the coefficients of a Kronecker
product of Schur functions stabilize. We also compute two new bounds for the stabilization of a sequence of coefficients and show that they improve existing bounds of M. Brion and E. Vallejo.
Briand, E., Orellana, R.C. y Rosas Celis, M.H. (2011). The stability of the Kronecker products of Schur functions. Journal of Algebra, 331 (1), 11-27.
0021-8693
http://hdl.handle.net/11441/41688
10.1016/j.jalgebra.2010.12.026
https://idus.us.es/xmlui/handle/11441/41688
The stability of the Kronecker products of Schur functions
oai:idus.us.es:11441/475842024-02-13T22:03:59Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2012-04
We give an algorithm which decides the Nielsen-Thurston type of a given four-strand braid. The complexity of our algorithm is quadratic with respect to word length. The proof of its validity is based on a result which states that for a reducible 4-braid which is as short as possible within its conjugacy class (short in the sense of Garside), reducing curves surrounding three punctures must be round or almost round. As an application, we give a polynomial time solution to the conjugacy problem for non-pseudo-Anosov
four-strand braids.
Calvez, M. y Wiest, B. (2012). Fast algorithmic Nielsen-Thurston classification of four-strand braids. Journal of Knot Theory and Its Ramifications, 21 (5), 1250043-1-1250043-25.
0218-2165
1793-6527
http://hdl.handle.net/11441/47584
10.1142/S0218216511009959
https://idus.us.es/xmlui/handle/11441/47584
Braid
Reducible braid
Nielsen-Thurston classification
Algorithm
Fast algorithmic Nielsen-Thurston classification of four-strand braids
oai:idus.us.es:11441/1386622024-02-13T10:04:31Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2019-04-09
We consider the p-center problem on tree graphs where the customers are modeled as continua subtrees. We address unweighted and weighted models as well as distances with and without addends. We prove that a relatively simple modification of Handler’s classical linear time algorithms for unweighted 1- and 2-center problems with respect to point customers, linearly solves the unweighted 1- and 2-center problems with addends of the above subtree customer model. We also develop polynomial time algorithms for the p-center problems based on solving covering problems and searching over special domains.
Fernández Fernández, M.C. (2019). On the local monodromy of AA-hypergeometric functions and some monodromy invariant subspaces. Revista matemática iberoamericana, 35 (3), 949-961. https://doi.org/10.4171/RMI/1085.
0213-2230
2235-0616
https://hdl.handle.net/11441/138662
10.4171/RMI/1085
On the local monodromy of AA-hypergeometric functions and some monodromy invariant subspaces
oai:idus.us.es:11441/563842024-02-13T09:24:16Zcom_11441_10978com_11441_10802com_11441_10690com_11441_10803col_11441_10979col_11441_10804
00925njm 22002777a 4500
dc
2016
Let E be an elliptic curve defined over Q. We study the relationship between the torsion subgroup E(Q)tors and the torsion subgroup E(K)tors, where K is
a cubic number field. In particular, we study the number of cubic number fields K such that E(Q)tors ̸= E(K)tors.
González Jiménez, E., Najman, F. y Tornero Sánchez, J.M. (2016). Torsion of rational elliptic curves over cubic fields. Rocky Mountain Journal of Mathematics, 46 (6), 1899-1917.
0035-7596
http://hdl.handle.net/11441/56384
10.1216/RMJ-2016-46-6-1899
Elliptic curves
Torsion subgroup
Rationals
Cubic fields
Torsion of rational elliptic curves over cubic fields
oai:idus.us.es:11441/866522024-02-15T07:50:14Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2019-05
We exhibit a rigid local system of rank six on the affine line in characteristic p = 5 whose arithmetic and geometric monodromy groups are the finite group 2.J2 (J2 the Hall-Janko
sporadic group) in one of its two (Galois-conjugate) irreducible representation of degree six.
Katz, N.M. y Rojas León, A. (2019). A rigid local system with monodromy group 2.J2. Finite Fields and Their Applications, 57, 276-286.
1071-5797
https://hdl.handle.net/11441/86652
10.1016/j.ffa.2019.02.008
Monodromy
Exponential sums
Representations of sporadic groups
A rigid local system with monodromy group 2.J2
oai:idus.us.es:11441/419792024-02-13T20:25:31Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2003
The following problem is treated: Characterizing the tangent cone and the equimultiple locus of a Puiseux surface (that is, an algebroid embedded surface admitting an equation whose roots are Puiseux power series), using a set of exponents appearing in a root of an equation. The aim is knowing to which extent the well–known results for the quasi–ordinary case can be extended to this much wider family.
Tornero Sánchez, J.M. (2003). Some geometric aspects of Puiseux surfaces. Revista Matemática Iberoamericana, 19 (2), 731-744.
0213-2230
2235-0616
http://hdl.handle.net/11441/41979
10.4171/RMI/366
https://idus.us.es/xmlui/handle/11441/41979
Algebroid surface
Puiseux power series
Some geometric aspects of Puiseux surfaces
oai:idus.us.es:11441/236052024-02-13T09:38:56Zcom_11441_10803com_11441_10802com_11441_10690com_11441_10893col_11441_10804col_11441_10896
00925njm 22002777a 4500
dc
2006
Sudoku is a logic-based placement puzzle. We recall how to
translate this puzzle into a 9-colouring problem which is
equivalent to a (big) algebraic system of polynomial equations. We
study how far Gröbner bases techniques can be used to treat
these systems produced by Sudokus. This general purpose tool can
not be considered as a good solver, but we show that it can be
useful to provide information on systems that are ---in spite of
their origin--- hard to solve.
978-3-540-45182-2
http://hdl.handle.net/11441/23605
https://idus.us.es/xmlui/handle/11441/23605
Gröbner bases
system of polynomial equations
Sudokus and Gröbner Bases: not only a Divertimento
oai:idus.us.es:11441/784722024-02-12T21:58:04Zcom_11441_10893com_11441_10802com_11441_10690com_11441_10803col_11441_10894col_11441_10804
00925njm 22002777a 4500
dc
2016
Gago Vargas, M.J. y Hartillo Hermoso, I. (2016). Álgebra computacional y programación entera no lineal. La Gaceta de la Real Sociedad Matemática Española, 19 (2), 363-375.
1138-8927
https://hdl.handle.net/11441/78472
Álgebra computacional
Programación entera no lineal
Álgebra computacional y programación entera no lineal
oai:idus.us.es:11441/1391562024-02-17T17:12:46Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2020-07-28
In this paper we revisit Ribenboim's notion of higher derivations of modules and relate it to the recent work of De Fernex and Docampo on the sheaf of differentials of the arc space. In particular, we derive their formula for the Kähler differentials of the Hasse-Schmidt algebra as a consequence of the fact that the Hasse-Schmidt algebra functors commute.
Chiu, C.H. y Narváez Macarro, L. (2020). Higher derivations of modules and the Hasse-Schmidt module. https://doi.org/10.48550/arXiv.2007.14171.
https://hdl.handle.net/11441/139156
10.48550/arXiv.2007.14171
Commutative Algebra
Algebraic Geometry
Representation Theory
Higher derivations of modules and the Hasse-Schmidt module
oai:idus.us.es:11441/475962024-02-14T09:10:52Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2012
The geometric motivic Poincaré series of a variety, which was introduced by Denef and Loeser, takes into account the classes in the Grothendieck ring of the sequence of jets of arcs in the variety. Denef and Loeser proved that this series has a rational form. We describe it in the case of an affine toric variety of arbitrary dimension. The result, which provides an explicit set of candidate
poles, is expressed in terms of the sequence of Newton polyhedra of certain monomial ideals, which we call logarithmic jacobian ideals, associated to the modules of differential forms with logarithmic poles outside the torus of the toric variety.
Cobo Pablos, H. y González Pérez, P.D. (2012). Motivic Poincaré series, toric singularities and logarithmic Jacobian ideals. Journal of Algebraic Geometry, 21 (3), 495-529.
1056-3911
1534-7486
http://hdl.handle.net/11441/47596
10.1090/S1056-3911-2011-00567-5
https://idus.us.es/xmlui/handle/11441/47596
Geometric motivic Poincaré series
Toric geometry
Singularities
Arc spaces
Motivic Poincaré series, toric singularities and logarithmic Jacobian ideals
oai:idus.us.es:11441/416932024-02-13T09:50:34Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2006
Consider the algebra Qhhx1, x2, . . .ii of formal power series in countably many noncommuting variables over the rationals. The subalgebra Π(x1, x2, . . .) of symmetric functions in noncommuting variables consists of all elements invariant under permutation of the variables and of bounded degree. We develop a theory of such functions analogous to the ordinary theory of symmetric functions. In particular, we define analogs of the monomial, power sum, elementary, complete homogeneous, and Schur
symmetric functions as will as investigating their properties.
Rosas Celis, M.H. y Sagan, B.E. (2006). Symmetric functions in noncommuting variables. Transactions of the American Mathematical Society, 358 (1), 215-232.
0002-9947
1088-6850
http://hdl.handle.net/11441/41693
10.1090/S0002-9947-04-03623-2
https://idus.us.es/xmlui/handle/11441/41693
noncommuting variables
partition lattice
Schur function
symmetric function
Symmetric functions in noncommuting variables
oai:idus.us.es:11441/1524282024-02-13T20:01:53Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2019-09-28
We prove that the spectrum constructed by González-Meneses, Manchón and the second author is stably homotopy equivalent to the Khovanov spectrum of Lipshitz and Sarkar at its extreme quantum grading.
0213-2230
2235-0616
https://hdl.handle.net/11441/152428
10.4171/rmi/1142
Extreme Khovanov spectra
oai:idus.us.es:11441/484392024-02-14T13:26:33Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2002-03
Let D, x be a plane curve germ. We prove that the complex Ω•(log D)x computes the cohomology of the complement of D, x only if D is quasihomogeneous. This is a partial converse to a theorem of F.J. Castro-Jiménez, D. Mond and L. Narváez-Macarro. Cohomology of the
complement of a free divisor. Transactions of the A.M.S., 348 (1996), 3037–
3049, which asserts that this complex does compute the cohomology of the
complement, whenever D is a locally weighted homogeneous free divisor
(and so in particular when D is a quasihomogeneous plane curve germ). We also give an example of a free divisor in D ⊂ C3 which is not locally weighted homogeneous, but for which this (second) assertion continues to hold.
Calderón Moreno, F.J., Mond, D., Narváez Macarro, L. y Castro Jiménez, F.J. (2002). Logarithmic cohomology of the complement of a plane curve. Commentarii Mathematici Helvetici, 77 (1), 24-38.
0010-2571
1420-8946
http://hdl.handle.net/11441/48439
10.1007/s00014-002-8330-6
https://idus.us.es/xmlui/handle/11441/48439
Free divisor
Logarithmic de Rham complex
Plane curve
Local quasi-homogeneity
Logarithmic cohomology of the complement of a plane curve
oai:idus.us.es:11441/1391092024-02-12T22:13:42Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2018-04-10
Artin–Tits groups act on a certain delta-hyperbolic complex, called the “additional length complex”. For an element of the group, acting loxodromically on this complex is a property analogous to the property of being pseudo-Anosov for elements of mapping class groups. By analogy with a well-known conjecture about mapping class groups, we conjecture that “most” elements of Artin–Tits groups act loxodromically. More precisely, in the Cayley graph of a subgroup G of an Artin–Tits group, the proportion of loxodromically acting elements in a ball of large radius should tend to one as the radius tends to infinity. In this paper, we give a condition guaranteeing that this proportion stays away from zero. This condition is satisfied e.g. for Artin–Tits groups of spherical type, their pure subgroups and some of their commutator subgroups.
Cumplido Cabello, M. (2018). On loxodromic actions of Artin–Tits groups. Journal of pure and applied algebra, 223 (1), 340-348. https://doi.org/10.1016/j.jpaa.2018.03.013.
0022-4049
1873-1376
https://hdl.handle.net/11441/139109
10.1016/j.jpaa.2018.03.013
On loxodromic actions of Artin–Tits groups
oai:idus.us.es:11441/1344382024-02-14T13:29:12Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2022-04-18
We consider the Hodge filtration on the sheaf of meromorphic functions along free divisors for which the logarithmic comparison theorem holds. We describe the Hodge filtration steps as submodules of the order filtration on a cyclic presentation in terms of a special factor of the Bernstein–Sato polynomial of the divisor and we conjecture a bound for the generating level of the Hodge filtration. Finally, we develop an algorithm to compute Hodge ideals of such divisors and we apply it to some examples.
1420-9020
https://hdl.handle.net/11441/134438
10.1007/s00029-022-00767-1
Hodge filtration
Hodge ideals
free divisors
Hodge ideals of free divisors
oai:idus.us.es:11441/475232024-02-17T17:49:35Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2014-09
We present an algorithm for solving the conjugacy search problem in the fourstrand braid group. The computational complexity is cubic with respect to the braid length.
Calvez, M. y Wiest, B. (2014). A fast solution to the conjugacy problem in the four-strand braid group. Journal of Group Theory, 17 (5), 757-780.
1433-5883
1435-4446
http://hdl.handle.net/11441/47523
10.1515/jgth-2014-0020
https://idus.us.es/xmlui/handle/11441/47523
A fast solution to the conjugacy problem in the four-strand braid group
oai:idus.us.es:11441/792092024-02-13T20:07:02Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2018
We give explicit formulas for the local multiplicative convolution functors, which express the local monodromies of the convolution of two ℓ-adic sheaves on the torus Gm over the algebraic closure of a finite field in terms of the local monodromies of the factors. As a particular case, we recover Fu’s formulas for the local Fourier transform.
Rojas León, A. (2018). Explicit local multiplicative convolution of ℓ-adic sheaves. Revista Matemática Iberoamericana, 34 (3), 1373-1386.
0213-2230
https://hdl.handle.net/11441/79209
10.4171/RMI/1027
ℓ-adic cohomology
Convolution
Galois representations of local fields
Explicit local multiplicative convolution of ℓ-adic sheaves
oai:idus.us.es:11441/422552024-02-15T07:27:39Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2014-10
An embedding of the m-times punctured disc into the n-times punctured
disc, for n > m, yields an embedding of the braid group on m strands Bm into the braid group on n strands Bn, called a geometric embedding. The main example consists of adding n−m trivial strands to the right of each braid on m strands. We show that geometric embeddings do not merge conjugacy classes, meaning that if the images of two elements in Bm by a geometric embedding are conjugate in Bn, the original elements are conjugate in Bm. We also show that the result does not hold, in general, for geometric embeddings of mapping class groups.
González-Meneses López, J. (2014). Geometric embeddings of braid groups do not merge conjugacy classes. Boletín de la Sociedad Matemática Mexicana, 20 (2), 297-305.
1405-213X
2296-4495
http://hdl.handle.net/11441/42255
http://dx.doi.org/10.1007/s40590-014-0018-6
https://idus.us.es/xmlui/handle/11441/42255
braid groups
mapping class groups
conjugacy classes
Geometric embeddings of braid groups do not merge conjugacy classes
oai:idus.us.es:11441/491212024-02-14T11:09:37Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2002
We give presentations, in terms of generators and relations, for the monoids SBn(M) of singular braids on closed surfaces. The proof of the validity of these presentations can also be applied to verify, in a new way, the presentations given by Birman for the monoids of Singular Artin braids.
González-Meneses López, J. (2002). Presentations for the monoids of singular braids on closed surfaces. Communications in Algebra, 30 (6), 2829-2836.
0092-7872
1532-4125
http://hdl.handle.net/11441/49121
10.1081/AGB-120003991
https://idus.us.es/xmlui/handle/11441/49121
Braid
Singular braid
Surface
Monoid
Presentation
Presentations for the monoids of singular braids on closed surfaces
oai:idus.us.es:11441/420472024-02-14T20:15:18Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2013
The dimension of the space of holomorphic solutions at nonsingular
points (also called the holonomic rank) of a A–hypergeometric system
MA(β) is known to be bounded above by 22d vol(A) [SST00], where d is the
rank of the matrix A and vol(A) is its normalized volume. This bound was
thought to be very vast because it is exponential on d. Indeed, all the examples we have found in the literature verify that rank(MA(β)) < 2vol(A).
We construct here, in a very elementary way, some families of matrices
A(d) ∈ Z d×n and parameter vectors β(d) ∈ C d , d ≥ 2, such that rank(MA(d)
(β(d) )) ≥ a dvol(A(d) ) for certain a > 1.
Fernández Fernández, M.C. (2013). Exponential growth of rank jumps for A-hypergeometric systems. Revista Matemática Iberoamericana, 29 (4), 1397-1404.
0213-2230
2235-0616
http://hdl.handle.net/11441/42047
http://dx.doi.org/10.4171/rmi/761
https://idus.us.es/xmlui/handle/11441/42047
Hypergeometric
D-module
holonomic rank
Exponential growth of rank jumps for A-hypergeometric systems
oai:idus.us.es:11441/1402672024-02-14T20:22:10Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2019-06-01
A Dwork family is a one-parameter monomial deformation of a Fermat hypersurface. In this paper we compute algebraically the invariant part of its Gauss-Manin cohomology under the action of certain subgroup of automorphisms. To achieve that goal we use the algebraic theory of D-modules, especially one-dimensional hypergeometric ones.
Castaño Domínguez, A. (2019). Dwork families and D-modules. Revista matemática iberoamericana, 35 (5), 1451-1484. https://doi.org/10.4171/rmi/1088.
https://hdl.handle.net/11441/140267
10.4171/rmi/1088
Dwork families and D-modules
oai:idus.us.es:11441/841832024-02-14T19:12:13Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2018-11
We study the centralizer of a braid from the point of view of Garside theory,
showing that generically a minimal set of generators can be computed very efficiently, as the ultra summit set of a generic braid has a very particular structure. We present an algorithm to compute the centralizer of a braid whose generic-case complexity is quadratic on the length of the input, and which outputs a minimal set of generators in the generic case.
González-Meneses López, J. y Valladares García, D. (2018). On the centralizer of generic braids. Journal of Group Theory, 21 (6), 973-1000.
1433-5883
1435-4446
https://hdl.handle.net/11441/84183
10.1515/jgth-2018-0027
Generic braids
On the centralizer of generic braids
oai:idus.us.es:11441/484352024-02-14T13:30:17Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2001-10-24
We extend to the analytic D-module case our results in the algebraic case, namely, we associate with any monogeneous module over the ring D of germs of linear differential operators at the origin of Cn, with holomorphic coefficients, a combinatorial object which we call the standard fan of this D-module (see chapter 6 for a precise geometric description of this object). The main tool of the proof is the homogenization techniques and a convergent division theorem that we prove in the homogenization ring D[t].
Assi, A., Castro Jiménez, F.J. y Granger, M. (2001). The analytic standard fan of a D-module. Journal of Pure and Applied Algebra, 164 (1-2), 3-21.
0022-4049
http://hdl.handle.net/11441/48435
10.1016/S0022-4049(00)00142-0
https://idus.us.es/xmlui/handle/11441/48435
The analytic standard fan of a D-module
oai:idus.us.es:11441/430852024-02-13T20:07:31Zcom_11441_10803com_11441_10802com_11441_10690col_11441_10804
00925njm 22002777a 4500
dc
2009-12-01
We will give algorithms of computing bases of logarithmic cohomology
groups for square-free polynomials in two variables.
Castro Jiménez, F.J. y Takayama, N. (2009). The computation of the logarithmic cohomology for plane curves. Journal of Algebra, 322 (11), 3839-3851.
0021-8693
1090-266X
http://hdl.handle.net/11441/43085
10.1016/j.jalgebra.2009.03.039
https://idus.us.es/xmlui/handle/11441/43085
algebraic geometry
Gröbner basis
logarithmic cohomology groups
curves
D-modules
The computation of the logarithmic cohomology for plane curves
marc///col_11441_10804/100