ﻻ يوجد ملخص باللغة العربية
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 $J_{0}(N)$, and we derive non-trivial remarks about the conjecture.
Let F be a finite extension of Qp, O_F its ring of integers and E a finite extension of Fp. The natural action of the unit group O_F* on O_F extends in a continuous action on the Iwasawa algebra E[[O_F]]. In this work, we show that non zero ideals of
We prove a special case of a dynamical analogue of the classical Mordell-Lang conjecture. In particular, let $phi$ be a rational function with no superattracting periodic points other than exceptional points. If the coefficients of $phi$ are algebrai
In this paper, we prove the Uniform Mordell-Lang Conjecture for subvarieties in abelian varieties. As a byproduct, we prove the Uniform Bogomolov Conjecture for subvarieties in abelian varieties.
This expository survey is based on my online talk at the ICCM 2020. It aims to sketch key steps of the recent proof of the uniform Mordell-Lang conjecture for curves embedded into Jacobians (a question of Mazur). The full version of this conjecture i
This survey article is the written version of a talk given at the Bourbaki seminar in April 2021. We give an introduction to Zagiers conjecture on special values of Dedekind zeta functions, and its relation to $K$-theory of fields and the theory of m