On the Geometry of a Siegel Modular Threefold.
On the p-rank of an abelian variety and its endomorphism algebra.
Let A be an abelian variety defined over a finite field. In this paper, we discuss the relationship between the p-rank of A, r(A), and its endomorphism algebra, End0(A). As is well known, End0(A) determines r(A) when A is an elliptic curve. We show that, under some conditions, the value of r(A) and the structure of End0(A) are related. For example, if the center of End0(A) is an abelian extension of Q, then A is ordinary if and only if End0(A) is a commutative field. Nevertheless, we give an example...
On the problem of detecting linear dependence for products of abelian varieties and tori
On the Rational Points of Abelian Varieties over Zp Extensions of Number Fields.
On the reduction of abelian varieties
-adic heights for semi-stable abelian varieties
-adic representations arising from descent on abelian varieties
-adic Teichmüller space and Siegel halfspace
p-Adic Height Pairings I.
p-adic height pairings. II.
P-division points on certain elliptic curves
Periods of p-adic Schottky groups.
Points de Heegner et derivées de fonctions L p-adiques.
Points de torsion sur les sous-variétés de groupes algébriques
Points d'ordre fini des variétés abéliennes de dimension un
Points rationnels d'ordre fini des courbes abéliennes (thèse d'Yves Hellegouarch)
Preuve des conjectures de Tate et de Shafarevitch
Pseudo-abelian varieties
Chevalley’s theorem states that every smooth connected algebraic group over a perfect field is an extension of an abelian variety by a smooth connected affine group. That fails when the base field is not perfect. We define a pseudo-abelian variety over an arbitrary field to be a smooth connected -group in which every smooth connected affine normal -subgroup is trivial. This gives a new point of view on the classification of algebraic groups: every smooth connected group over a field is an extension...
Quelques applications du théorème de densité de Chebotarev
Quelques travaux récents en théorie des nombres transcendants