Decomposing Jacobians of curves with extra automorphisms
Definable sets over finite fields.
Deformations and derived categories
In this paper we generalize the deformation theory of representations of a profinite group developed by Schlessinger and Mazur to deformations of objects of the derived category of bounded complexes of pseudocompact modules for such a group. We show that such objects have versal deformations under certain natural conditions, and we find a sufficient condition for these versal deformations to be universal. Moreover, we consider applications to deforming Galois cohomology classes and the étale hypercohomology...
Degeneration of polylogarithms and special values of -functions for totally real fields.
Degré d’une extension de sur laquelle est semi-stable
Soit un entier . Pour un nombre premier on note l’extension maximale non ramifiée de . Supposons que divise exactement . Alors, en utilisant les travaux de Carayol et la théorie du corps de classes local, on détermine une extension de sur laquelle la jacobienne de la courbe modulaire de admet une réduction semi-stable, puis on donne une estimation de son degré.
D-elliptic sheaves and the Langlands correspondence.
Denominators of Igusa class polynomials
In [22], the authors proved an explicit formula for the arithmetic intersection number on the Siegel moduli space of abelian surfaces, under some assumptions on the quartic CM field . These intersection numbers allow one to compute the denominators of Igusa class polynomials, which has important applications to the construction of genus curves for use in cryptography. One of the main tools in the proof was a previous result of the authors [21] generalizing the singular moduli formula of Gross...
Density of rational points on elliptic fibrations-II
Derivatives of Eisenstein series and generating functions for arithmetic cycles
Des nombres premiers à la géométrie algébrique (une brève histoire de la fonction zêta)
Des obstructions globales à la descente des revêtements
Descent via (3,3)-isogeny on Jacobians of genus 2 curves
We give a parametrization of curves C of genus 2 with a maximal isotropic (ℤ/3)² in J[3], where J is the Jacobian variety of C, and develop the theory required to perform descent via (3,3)-isogeny. We apply this to several examples, where it is shown that non-reducible Jacobians have non-trivial 3-part of the Tate-Shafarevich group.
Descente infinie et hauteur p-adique sur les courbes elliptiques à multiplication complexe.
Dessins d'enfants: bipartite maps and Galois groups.
Détermination de certains cas généraux où l’équation n’admet pas de solution en nombres entiers
Détermination de courbes elliptiques pour la conjecture de Szpiro
Determination of elliptic curves with everywhere good reduction over ℚ(√37)
Determination of elliptic curves with everywhere good reduction over real quadratic fields ℚ(√(3p))
Die complexe Multiplication der Thetafunctionen
Die Fundamentalgruppen Siegelscher Modulvarietäten.