Fabien Pazuki

Elementary 3-descent with a 3-isogeny

In this expository paper, we show how to use in practice 3-descent with a 3-isogeny to find an estimate for the rank of an elliptic curve having a rational 3-torsion subgroup, and we also give a geometric interpretation of these computations.

Remarques sur une conjecture de Lang

The aim of this paper is to study a conjecture predicting a lower bound on the canonical height on abelian varieties, formulated by S. Lang and generalized by J. H. Silverman. We give here an asymptotic result on the height of Heegner points on the modular jacobian

POLARIZED MORPHISMS BETWEEN ABELIAN VARIETIES

J_{0}(N)

Theta height and Faltings height

, and we derive non-trivial remarks about the conjecture.

Zhang's conjecture and squares of Abelian surfaces

We study in this paper some criterions to get polarized morphisms between abelian varieties. We deduce explicit dynamical systems with particular intersection properties.