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Pilar Pisón Casares, in memoriam
(Real Sociedad Matematica Española, 2007)
Estamos habituados a describir objetos matemáticos, a elaborar teorías, conjeturar resultados, demostrar asertos o refutar hipótesis, pero no a escribir de una persona, más aún si con ella tenemos vínculos afectivos que ...
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Torsion of rational elliptic curves over quadratic fields
(Springer, 2014-09)
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 quadratic number field.
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A complete diophantine characterization of the rational torsion of an elliptic curve
(Springer, 2012-01)
We give a complete characterization for the rational torsion of an elliptic curve in terms of the (non–)existence of integral solutions of a system of diophantine equations.
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Specializations of MacMahon symmetric functions and the polynomial algebra
(Elsevier, 2002-03-06)
A MacMahon symmetric function is a formal power series in a finite number of alphabets that is invariant under the diagonal action of the symmetric group. We use a combinatorial construction of the different bases of the ...
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Exponents of Some One-Dimensional Gauss–Manin Systems
(European Mathematical Society Publishing House, 2017-07-03)
In this paper we provide a purely algebraic characterization of the exponents of one-dimensional direct images of a structure sheaf by a rational function, related to the vanishing of the cohomologies of a certain Koszul ...
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Rectangular symmetries for coe cients of symmetric functions
(The Electronic Journal of Combinatorics, 2015-07-31)
We show that some of the main structural constants for symmetric functions (Littlewood-Richardson coe cients, Kronecker coe cients, plethysm coe cients, and the Kostka{Foulkes polynomials) share symmetries related to the ...
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Dualité et comparaison sur les complexes de de Rham logarithmiques par rapport aux diviseurs libres
(Association des Annales de l'Institut Fourier, 2005)
Let X be a complex analytic manifold and D \subset X a free divisor. Integrable logarithmic connections along D can be seen as locally free {\cal O}_X-modules endowed with a (left) module structure over the ring of logarithmic ...
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Rings of differential operators as enveloping algebras of Hasse–Schmidt derivations
(Elsevier, 2020-01)
Let k be a commutative ring and A a commutative k-algebra. In this paper we introduce the notion of enveloping algebra of Hasse–Schmidt derivations of A over k and we prove that, under suitable smoothness hypotheses, the ...
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Conservation of the noetherianity by perfect transcendental field extensions
(European Mathematical Society, 2003)
Let k be a perfect field of characteristic p>0, k(t)per the perfect closure of k(t) and A a k-algebra. We characterize whether the ring A⊗kk(t)per is noetherian when A is the ring of formal power series in n indeterminates over k.
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Gröbner δ-bases and Gröbner bases for differential operators
(Polish Academy of Sciences, Institute of Mathematics, 2002)
This paper deals with the notion of Gr¨obner δ-base for some rings of linear differential operators by adapting the works of W. Trinks, A. Assi, M. Insa and F. Pauer. We compare this notion with the one of Gröbner base for ...