Points de petite hauteur sur une variété semi-abélienne de la forme ${\mathbb{G}}_m^n\times A$

Abstract

Recently, Rémond stated a very general conjecture on lower bounds of a normalized height on either an abelian variety or a power of the multiplicative group. In this note, we extend a particular case of this conjecture to split semi-abelian varieties of the form ${\mathbb{G}}_m^n\times A$. This allows us to connect many results already existing in the litterature. Finally, we give new examples for which this conjecture holds.

Final version. in French language. Published in Bull. Lond. Math. Soc. NB: this version is slightly different from the one published http://doi.org/10.1112/blms.12693

References in corpus (1)

• Small Height and Infinite Non-Abelian Extensions

Cited by in corpus (1)

• On the Northcott property for special values of L-functions