Remarques sur une conjecture de Lang

TL;DR

This paper investigates a conjecture by Lang and Silverman on lower bounds for canonical heights on abelian varieties, providing asymptotic results for Heegner points and offering insights into the conjecture's validity.

Contribution

It presents an asymptotic analysis of Heegner points' heights on modular Jacobians, contributing new remarks on Lang's conjecture.

Findings

Asymptotic behavior of heights of Heegner points analyzed

Non-trivial remarks on Lang's conjecture derived

Insights into the lower bounds of canonical heights provided

Abstract

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.