Le probleme de Bogomolov effectif sur les varietes abeliennes

TL;DR

This paper establishes a new lower bound for the essential minimum of certain subvarieties in abelian varieties, contingent on a conjecture about ordinary primes, extending known results from the toric case.

Contribution

It introduces a novel lower bound for the essential minimum on abelian varieties with small codimension, assuming a conjecture about ordinary primes.

Findings

New lower bound for essential minimum under conjecture

Extension of toric case results to abelian varieties

Optimal bound up to epsilon in degree

Abstract

We give a new lower bound for the essential minimum of subvarieties of abelian varieties with small codimension, under a conjecture about ordinary primes in abelian varieties. This lower bound is already known in the toric case since the work of Amoroso and David. It is the best expected, "up to an epsilon", in the degree of the subvariety.