Points of small height on semiabelian varieties

authored by

Lars Kühne

Abstract

The equidistribution conjecture is proved for general semiabelian varieties over number fields. Previously, this conjecture was only known in the special case of almost split semiabelian varieties through work of Chambert-Loir. The general case has remained intractable so far because the height of a semiabelian variety is negative unless it is almost split. In fact, this places the conjecture outside the scope of Yuan's equidistribution theorem on algebraic dynamical systems. To overcome this, an asymptotic adaption of the equidistribution technique invented by Szpiro, Ullmo, and Zhang is used here. It also allows a new proof of the Bogomolov conjecture and hence a self-contained proof of the strong equidistribution conjecture in the same general setting.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

Type

Article

Journal

Journal of the European Mathematical Society

Volume

24

Pages

2077-2131

No. of pages

55

ISSN

1435-9855

Publication date

25.09.2022

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Mathematics(all), Applied Mathematics

Electronic version(s)

https://doi.org/10.4171/JEMS/1125 (Access: Open)