Points de petite hauteur sur les varietes semi-abeliennes

Abstract

We extend to the case of semi-abelian varieties the statements of various variants of the conjecture alla Bogomolov about the non-density of small points of small height in abelian varieties. Inspired by recent work of Ullmo, Zhang and Bilu, we then prove these conjectures when the semi-abelian variety is almost split. The proof uses Arakelov geometry and equirepartition arguments.