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Improvements of the Weil bound for Artin-Schreier curves
(Springer, 2011-10)
For the Artin-Schreier curve y q − y = f(x) defined over a finite field Fq of q elements, the celebrated Weil bound for the number of Fq r -rational points can be sharp, especially in super-singular cases and when r is ...
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Grothendieck bialgebras, Partition lattices, and symmetric functions in noncommutative variables
(American Mathematical Society, 2006)
We show that the Grothendieck bialgebra of the semi-tower of partition lattice algebras is isomorphic to the graded dual of the bialgebra of symmetric functions in noncommutative variables. In particular this isomorphism ...
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Purity of exponential sums on An
(Kluwer, 2006-03)
We give a purity result for two kinds of exponential sums of the type ∑x∈knψ(f(x)), where k is a finite field of characteristic p and ψ:k→C⋆ is a non-trivial additive character. In the first case, f∈k[x1,…,xn] is a polynomial ...
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Hironaka's characteristic polygon and effective resolution of surfaces
(Elsevier, 2007-03-01)
Hironaka’s concept of characteristic polyhedron of a singularity has been one of the most powerful and fruitful ideas of the last decades in singularity theory. In fact, since then combinatorics have become a major tool ...
PhD Thesis
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Descripción explícita de t-estructuras sobre espacios estratificados
(2000)
"En el presenta trabajo abordamos la cuestión anterior de la descripción de las categorías de haces perversos desde un punto de vista general y puramente topológico, desarrollando el método iniciado en [NM94], y poniendo ...
PhD Thesis
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Métodos efectivos en anillos de operadores diferenciales y en sistemas hipergeométricos
(2002)
El Análisis Algebraico, o teoría de D-m&oa cute;dulos, trata el estudio de los sistemas de ecuaciones -- en derivadas parciales desde el punto de vista del álgebra y la geometría. Esta teoría generalizada la teoría clásica ...
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Compatible systems of symplectic Galois representations and the inverse Galois problem II. Transvections and huge image
(Mathematical Sciences Publishers, 2016-03)
This article is the second part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. This part is concerned with symplectic Galois ...
PhD Thesis
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Operadores diferenciales logarítmicos con respecto a un divisor libre
(1997)
En esta memoria estudiamos la V-filtración relativa a divisores libres en una variedad analítica compleja lisa de dimensión arbitraria. Más concretamente abordamos la estructura de los operadores diferenciales en el término ...
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Basic results on braid groups
(Université Blaise Pascal, 2011)
These are Lecture Notes of a course given by the author at the French-Spanish School Tresses in Pau, held in Pau (France) in October 2009. It is basically an introduction to distinct approaches and techniques that can be ...
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Fonctions zêta ℓ-modulaires
(Duke University Press, 2012)
Soient F un corps commutatif localement compact non archimédien, de caractéristique résiduelle notée p, et D une F-algèbre à division centrale de dimension finie. Soit un nombre premier différent de p. Dans cet ...