Points de petite hauteur sur une vari\'et\'e semi-ab\'elienne de la forme ${\mathbb{G}}_m^n\times A$

Recently, R'emond 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.