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