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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 ...
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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 ...
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Locally quasi-homogeneous free divisors are Koszul free
(MAIK Nauka/Interperiodica, 2002)
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 ...
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Combinatorics on a family of reduced Kronecker coefficients
(Elsevier, 2015-10)
The reduced Kronecker coefficients are particular instances of Kronecker coefficients that contain enough information to recover them. In this notes we compute the generating function of a family of reduced Kronecker ...
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Reduced Kronecker coefficients and counter-examples to Mulmuley's strong saturation conjecture SH
(Springer, 2009-12)
We provide counter–examples to Mulmuley’s strong saturation conjecture (strong SH) for the Kronecker coefficients. This conjecture was proposed in the setting of Geometric Complexity Theory to show that deciding whether ...
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Decomposing Jacobians of curves over finite fields in the absence of algebraic structure
(Elsevier, 2015-11)
We consider the issue of when the L-polynomial of one curve over Fq divides the L-polynomial of another curve. We prove a theorem which shows that divisibility follows from a hypothesis that two curves have the same number ...
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Large Galois images for Jacobian varieties of genus 3 curves
(Polish Academy of Sciences, Institute of Mathematics, 2016)
Given a prime number ℓ ≥ 5, we construct an infinite family of three-dimensional abelian varieties over Q such that, for any A/Q in the family, the Galois representation ρA,ℓ : GQ → GSp6 (Fℓ) attached to the ℓ-torsion of ...
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Compatible systems of symplectic Galois representations and the inverse Galois problem III. Automorphic construction of compatible systems with suitable local properties
(Springer, 2015-04)
This article is the third and last part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. This part proves the following new result ...
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The Gröbner fan of an An-module
(Elsevier, 2000-06-14)
Let I be a non-zero left ideal of the Weyl algebra An of order n over a field k and let L:R2n→R be a linear form defined by L(α,β)=∑i=1neiαi+∑i=1nfiβi. If ei+fi≥0, then L defines a filtration F•L on An. Let grL(I) be the ...