Rational Points of Abelian Varieties with Values in Towers of Number Fields.
Rational points on the modular curves
Real Abelian Varieties and the Theory of Comessatti.
Real algebraic curves
Reduction of the Manin map modulo p.
Refined theorems of the Birch and Swinnerton-Dyer type
In this paper, we generalize the context of the Mazur-Tate conjecture and sharpen, in a certain way, the statement of the conjecture. Our main result will be to establish the truth of a part of these new sharpened conjectures, provided that one assume the truth of the classical Birch and Swinnerton-Dyer conjectures. This is particularly striking in the function field case, where these results can be viewed as being a refinement of the earlier work of Tate and Milne.
Remarks on strongly modular Jacobian surfaces
In [3] we introduced the concept of strongly modular abelian variety. This note contains some remarks and examples of this kind of varieties, especially for the case of Jacobian surfaces, that complement the results of [3].
Rigid analytic spaces
Semistable reduction and torsion subgroups of abelian varieties
The main result of this paper implies that if an abelian variety over a field has a maximal isotropic subgroup of -torsion points all of which are defined over , and , then the abelian variety has semistable reduction away from . This result can be viewed as an extension of Raynaud’s theorem that if an abelian variety and all its -torsion points are defined over a field and , then the abelian variety has semistable reduction away from . We also give information about the Néron models...
Shimura Varieties and Twisted Orbital Integrals.
Siegel Cusp Forms as Holomorphic Differential Forms on Certain Compact Varieties.
Small values of the quadratic part of the Néron-Tate height on an abelian variety
Sous-groupes à plusieurs paramètres -adiques de variétés abéliennes
Sous-groupes canoniques et cycles évanescents p-adiques pour les variétés abéliennes
Stable reduction and uniformization of abelian varieties II.
Sur des hauteurs alternatives. I.
Sur les mauvais facteurs locaux des fonctions L attachées aux surfaces abéliennes et surfaces K-3
Systematic Growth of Mordell-Weil Groups of Abelian Varieties in Towers of Number Fields.
The Arithmetic Theory of Local Constants for abelian Varieties
The Cassels-Tate pairing on polarized Abelian varieties.