Equidistribution of torsion points in abelian varieties

TL;DR

This paper proves that torsion points in abelian varieties are evenly spread out over their associated Berkovich spaces, with respect to a natural measure, revealing a deep uniformity property.

Contribution

It establishes the equidistribution of torsion points in abelian varieties within the Berkovich space framework, a novel result linking arithmetic and non-Archimedean geometry.

Findings

Torsion points are equidistributed in the Berkovich space.

The distribution aligns with the canonical measure.

This links torsion points to geometric measure theory.

Abstract

We prove that the torsion points of an abelian variety are equidistributed over the corresponding berkovich space with respect to the canonical measure.