Points of small height on semiabelian varieties

verfasst von

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.

Organisationseinheit(en)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

Typ

Artikel

Journal

Journal of the European Mathematical Society

Band

24

Seiten

2077-2131

Anzahl der Seiten

55

ISSN

1435-9855

Publikationsdatum

25.09.2022

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Mathematik (insg.), Angewandte Mathematik

Elektronische Version(en)

https://doi.org/10.4171/JEMS/1125 (Zugang: Offen)