Homoth\'eties explicites des repr\'esentations $\ell$-adiques

TL;DR

This paper investigates the size of homothety subgroups in dic representations of abelian variety torsion points, providing explicit bounds relevant to the Manin-Mumford conjecture.

Contribution

It offers new explicit estimates on homothety subgroups and applies these to derive uniform bounds for the Manin-Mumford problem.

Findings

New bounds on homothety subgroups of dic representations

Explicit estimates for torsion points of abelian varieties

Uniform bounds for the Manin-Mumford conjecture

Abstract

We present classical and new results on the size of the subgroup of homotheties of $\ell$-adic representations associated to the torsion of an abelian variety. From these estimates, we derive uniform and explicit bounds for the Manin-Mumford problem.