A bound for the torsion on subvarieties of abelian varieties

TL;DR

This paper establishes a uniform bound on the degree of maximal torsion cosets within subvarieties of abelian varieties, utilizing algebraic interpolation and Serre's theorem on Galois representations.

Contribution

It introduces a new uniform bound for torsion cosets on subvarieties of abelian varieties, combining algebraic and Galois-theoretic techniques.

Findings

Established a uniform bound on torsion cosets.

Combined algebraic interpolation with Serre's theorem.

Provides a new tool for studying torsion structures.

Abstract

We give a uniform bound on the degree of the maximal torsion cosets for subvarieties of an abelian variety. The proof combines algebraic interpolation and a theorem of Serre on homotheties in the Galois representation associated to the torsion subgroup of an abelian variety.