Equidistribution of small subvarieties of an abelian variety

TL;DR

This paper extends the concept of equidistribution from small points to small subvarieties within abelian varieties, broadening the scope of previous results in arithmetic geometry.

Contribution

It generalizes the Szpiro-Ullmo-Zhang theorem to include small subvarieties, providing a new understanding of their distribution in abelian varieties.

Findings

Established equidistribution for small subvarieties

Generalized previous point-based results

Enhanced understanding of arithmetic distribution patterns

Abstract

We prove an equidistribution result for small subvarieties of an abelian variety which generalizes the Szpiro-Ullmo-Zhang theorem on equidistribution of small points.