Algebra

URI permanente para esta comunidadhttps://hdl.handle.net/11441/10803

Examinar

Mostrando 1 - 20 de 38

Abelian varieties over number fields, tame ramification and big Galois image
(International Press, 2013) Arias de Reyna Domínguez, Sara; Kappen, Christian; Universidad de Sevilla. Departamento de álgebra; Ministerio de Educación y Ciencia (MEC). España; Universidad de Sevilla. FQM218: Geometria Algebraica, Sistemas Diferenciales y Singularidades
Given a natural number n ≥ 1 and a number field K, we show the existence of an integer ℓ0 such that for any prime number ℓ ≥ ℓ0, there exists a finite extension F/K, unramified in all places above ℓ, together with a principally polarized abelian variety A of dimension n over F such that the resulting ℓ-torsion representation ρA,ℓ : GF → GSp(A[ℓ](F)) is surjective and everywhere tamely ramified. In particular, we realize GSp2n(Fℓ) as the Galois group of a finite tame extension of number fields F0/F such that F is unramified above ℓ.
Bi-orderings on pure braided Thompson's groups
(2008-03) Burillo Puig, José; González-Meneses López, Juan; Universidad de Sevilla. Departamento de álgebra; Ministerio de Educación y Ciencia (MEC). España; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)
In this paper it is proved that the pure braided Thompson’s group BF admits a bi-order, analog to the bi-order of the pure braid groups.
Coefficient fields and scalar extension in positive characteristic
(Elsevier, 2005-03-15) Fernández Lebrón, María Magdalena; Narváez Macarro, Luis; Universidad de Sevilla. Departamento de Matemática Aplicada I; Universidad de Sevilla. Departamento de álgebra; Ministerio de Educación y Ciencia (MEC). España; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER); Universidad de Sevilla. FQM218: Geometria Algebraica, Sistemas Diferenciales y Singularidades
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 .
Equimultiple locus of embedded algebroid surfaces and blowing-up in arbitrary characteristic
(Chinese Academy of Sciences, 2009-12) Piedra Sánchez, Ramón; Tornero Sánchez, José María; Universidad de Sevilla. Departamento de álgebra; Ministerio de Educación y Ciencia (MEC). España; Junta de Andalucía
This paper extends previous results of the authors, concerning the behaviour of the equimultiple locus of algebroid surfaces under blowing–up, to arbitrary characteristic.
Estimates for singular multiplicative character sums
(Duke University Press, 2005) Rojas León, Antonio; Universidad de Sevilla. Departamento de álgebra; Ministerio de Educación y Ciencia (MEC). España; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)
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.
Formal groups, supersingular abelian varieties and tame ramification
(Elsevier, 2011-05-15) Arias de Reyna Domínguez, Sara; Universidad de Sevilla. Departamento de álgebra; Ministerio de Educación y Ciencia (MEC). España; Universidad de Sevilla. FQM218: Geometria Algebraica, Sistemas Diferenciales y Singularidades
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.
Gevrey solutions of the irregular hypergeometric system associated with an affine monomial curve
(American Mathematical Society, 2011) Fernández Fernández, María Cruz; Castro Jiménez, Francisco Jesús; Universidad de Sevilla. Departamento de álgebra; Ministerio de Educación y Ciencia (MEC). España; Junta de Andalucía
We describe the Gevrey series solutions at singular points of the irregular hypergeometric system (GKZ system) associated with an affine monomial curve. We also describe the irregularity complex of such a system with respect to its singular support.
Hasse-Schmidt derivations, divided powers and differential smoothness
(Association des Annales de l'Institut Fourier, 2009) Narváez Macarro, Luis; Universidad de Sevilla. Departamento de álgebra; Ministerio de Educación y Ciencia (MEC). España; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER); Universidad de Sevilla. FQM218: Geometria Algebraica, Sistemas Diferenciales y Singularidades
Let k be a commutative ring, A a commutative k-algebra and D the filtered ring of k-linear differential operators of A. We prove that: (1) The graded ring gr D admits a canonical embedding θ into the graded dual of the symmetric algebra of the module ΩA/k of differentials of A over k, which has a canonical divided power structure. (2) There is a canonical morphism ϑ from the divided power algebra of the module of k-linear Hasse-Schmidt integrable derivations of A to gr D. (3) Morphisms θ and ϑ fit into a canonical commutative diagram.
Irregular hypergeometric D-modules
(E, 2010-08-01) Fernández Fernández, María Cruz; Universidad de Sevilla. Departamento de álgebra; Ministerio de Educación y Ciencia (MEC). España; Junta de Andalucía
We study the irregularity of hypergeometric D-modules MA(β) via the explicit construction of Gevrey series solutions along coordinate subspaces in X = C n. As a consequence, we prove that along coordinate hyperplanes the combinatorial characterization of the slopes of MA(β) given by M. Schulze and U. Walther in [25] still holds for any full rank integer matrix A. We also provide a lower bound for the dimensions of the spaces of Gevrey solutions along coordinate subspaces in terms of volumes of polytopes and prove the equality for very generic parameters. Holomorphic solutions outside the singular locus of MA(β) can be understood as Gevrey solutions of order one along X at generic points and so they are included as a particular case.
Le théorème du symbole total d’un opérateur différentiel p-adique
(Consejo Superior de Investigaciones Científicas, 2010) Mebkhout, Zoghman; Narváez Macarro, Luis; Universidad de Sevilla. Departamento de álgebra; Ministerio de Educación y Ciencia (MEC). España; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)
Let X † be a smooth †-scheme (in the sense of Meredith) over a complete discrete valuation ring (V,m) of unequal characteristics (0, p) and let D†X†/V be the sheaf of V -linear endomorphisms of OX† whose reduction modulo ms is a linear differential operator of order bounded by an affine function in s. In this paper we prove that locally there is an OX† -isomorphism between the sections of D†X†/V and the overconvergent total symbols, and we deduce a cohomological triviality property.
Localization at hyperplane arrangements: combinatorics and D-modules
(Elsevier, 2007-10-15) Álvarez Montaner, Josep; Castro Jiménez, Francisco Jesús; Ucha Enríquez, José María; Universidad de Sevilla. Departamento de álgebra; Ministerio de Educación y Ciencia (MEC). España; Junta de Andalucía; Universidad de Sevilla. FQM333: Algebra Computacional en Anillos no Conmutativos y Aplicaciones
We describe an algorithm deciding if the annihilating ideal of the meromorphic function 1 f , where f = 0 defines an arrangement of hyperplanes, is generated by linear differential operators of order 1. The algorithm is based on the comparison of two characteristic cycles and uses a combinatorial description due to Alvarez-Montaner, García–López and Zarzuela of the characteristic cycle of the D-module of meromorphic functions with respect to f.
Locally quasi-homogeneous free divisors are Koszul free
(MAIK Nauka/Interperiodica, 2002) Calderón Moreno, Francisco Javier; Narváez Macarro, Luis; Universidad de Sevilla. Departamento de álgebra; Ministerio de Educación y Ciencia (MEC). España; Universidad de Sevilla. FQM218: Geometría Algebraica, Sistemas Diferenciales y Singularidades
Let X be a complex analytic manifold and D ⊂ X be a free divisor. If D is locally quasi-homogeneous, then the logarithmic de Rham complex associated to D is quasi-isomorphic to Rj∗(CX\D), which is a perverse sheaf. On the other hand, the logarithmic de Rham complex associated to a Koszul-free divisor is perverse. In this paper, we prove that every locally quasi-homogeneous free divisor is Koszul free.
Logarithmic cohomology of the complement of a plane curve
(Springer, 2002-03) Calderón Moreno, Francisco Javier; Mond, David; Narváez Macarro, Luis; Castro Jiménez, Francisco Jesús; Universidad de Sevilla. Departamento de álgebra; Ministerio de Educación y Ciencia (MEC). España; Engineering and Physical Sciences Research Council (UK); Universidad de Sevilla. FQM218: Geometría Algebraica, Sistemas Diferenciales y Singularidades; Universidad de Sevilla. FQM333: Álgebra Computacional en Anillos no Conmutativos y Aplicaciones
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.
Maltsiniotis's first conjecture for K1
(Duke University Press, 2008) Muro Jiménez, Fernando; Universidad de Sevilla. Departamento de álgebra; Ministerio de Educación y Ciencia (MEC). España; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)
We show that K1(E) of an exact category E agrees with K1(DE) of the associated triangulated derivator DE. More generally we show that K1(W) of a Waldhausen category W with cylinders and a saturated class of weak equivalences agrees with K1(DW) of the associated right pointed derivator DW.
Milne's volume function and vector symmetric polynomials
(Elsevier, 2009-05) Briand, Emmanuel; Rosas Celis, Mercedes Helena; Universidad de Sevilla. Departamento de álgebra; Ministerio de Educación y Ciencia (MEC). España
The number of real roots of a system of polynomial equations fitting inside a given box can be counted using a vector symmetric polynomial introduced by P. Milne, the volume function. We provide the expansion of Milne’s volume function in the basis of monomial vector symmetric functions, and observe that only monomial functions of a particular kind appear in the expansion, the squarefree monomial functions. By means of an appropriate specialization of the vector symmetric Newton identities, we derive an inductive formula that expresses the squarefree monomial functions in the power sums basis. As a corollary, we obtain an inductive formula that writes Milne’s volume function in the power sums basis. The lattice of the sub–hypergraphs of an hypergraph appears in a natural way in this setting.
Motivic Poincaré series, toric singularities and logarithmic Jacobian ideals
(American Mathematical Society, 2012) Cobo Pablos, Helena; González Pérez, Pedro Daniel; Universidad de Sevilla. Departamento de álgebra; Ministerio de Educación y Ciencia (MEC). España; Fundación Caja Madrid; Universidad de Sevilla. FQM218: Geometria Algebraica, Sistemas Diferenciales y Singularidades
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.
On the cycling operation in braid groups
(Elsevier, 2008-09-06) González-Meneses López, Juan; Gebhardt, Volker; Universidad de Sevilla. Departamento de álgebra; Ministerio de Educación y Ciencia (MEC). España; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)
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.
On the functoriality of cohomology of categories
(Elsevier, 2006-03) Muro Jiménez, Fernando; Universidad de Sevilla. Departamento de álgebra; Ministerio de Educación y Ciencia (MEC). España
In this paper we show that the Baues-Wirsching complex used to define cohomology of categories is a 2-functor from a certain 2-category of natural systems of abelian groups to the 2-category of chain complexes, chain homomorphism and relative homotopy classes of chain homotopies. As a consequence we derive (co)localization theorems for this cohomology.
On the logarithmic comparison theorem for integrable logarithmic connections
(London Mathematical Society, 2009) Calderón Moreno, Francisco Javier; Narváez Macarro, Luis; Universidad de Sevilla. Departamento de álgebra; Ministerio de Educación y Ciencia (MEC). España; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER); Universidad de Sevilla. FQM218: Geometria Algebraica, Sistemas Diferenciales y Singularidades
Let X be a complex analytic manifold, D ⊂ X a free divisor with jacobian ideal of linear type (e.g. a locally quasi-homogeneous free divisor), j : U = X − D ֒→ X the corresponding open inclusion, E an integrable logarithmic connection with respect to D and L the local system of the horizontal sections of E on U. In this paper we prove that the canonical morphisms Ω • X(log D)(E(kD)) −→ Rj∗L, j!L −→ Ω • X(log D)(E(−kD)) are isomorphisms in the derived category of sheaves of complex vector spaces for k ≫ 0 (locally on X).
On the modules of m-integrable derivations in non-zero characteristic
(Elsevier, 2012-03-20) Narváez Macarro, Luis; Universidad de Sevilla. Departamento de álgebra; Ministerio de Educación y Ciencia (MEC). España; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER); Universidad de Sevilla. FQM218: Geometria Algebraica, Sistemas Diferenciales y Singularidades
Let k be a commutative ring and A a commutative k-algebra. Given a positive integer m, or m = ∞, we say that a k-linear derivation δ of A is m-integrable if it extends up to a Hasse–Schmidt derivation D = (Id, D1 = δ, D2, . . . , Dm) of A over k of length m. This condition is automatically satisfied for any m under one of the following orthogonal hypotheses: (1) k contains the rational numbers and A is arbitrary, since we can take Di = δ i i! ; (2) k is arbitrary and A is a smooth k-algebra. The set of m-integrable derivations of A over k is an A-module which will be denoted by Iderk(A; m). In this paper we prove that, if A is a finitely presented k-algebra and m is a positive integer, then a k-linear derivation δ of A is m-integrable if and only if the induced derivation δp : Ap → Ap is m-integrable for each prime ideal p ⊂ A. In particular, for any locally finitely presented morphism of schemes f : X → S and any positive integer m, the S-derivations of X which are locally mintegrable form a quasi-coherent submodule Ider S(OX; m) ⊂ Der S(OX) such that, for any affine open sets U = Spec A ⊂ X and V = Spec k ⊂ S, with f(U) ⊂ V , we have Γ(U,Ider S(OX; m)) = Iderk(A; m) and Ider S(OX; m)p = IderOS,f(p) (OX,p; m) for each p ∈ X. We also give, for each positive integer m, an algorithm to decide whether all derivations are m-integrable or not.

Examinar

Examinando Algebra por Agencia financiadora "Ministerio de Educación y Ciencia (MEC). España"