Equidistribution theorem over an adelic curve

TL;DR

This paper develops a new framework for adelic spaces over arithmetic varieties and proves an equidistribution theorem, with applications to Bogomolov-type results for Abelian varieties over adelic curves.

Contribution

It introduces the concept of global adelic space over an adelic curve and establishes an equidistribution theorem for subvarieties, extending previous arithmetic geometry results.

Findings

Proved an equidistribution theorem for subvarieties over adelic curves.

Established a Bogomolov type theorem for Abelian varieties.

Introduced the notion of global adelic space for arithmetic varieties.

Abstract

In this article, we introduce the notion of global adelic space of an arithmetic variety over an adelic curve and prove an equidistribution theorem for a generic sequence of subvarieties. As an application, we prove a Bogomolov type theorem for Abelian varieties over an adelic curve of characteristic 0.