English

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

Number Theory 2022-07-01 v4

Abstract

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 Gmn×A\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.

Keywords

Cite

@article{arxiv.1901.07980,
  title  = {Points de petite hauteur sur une vari\'et\'e semi-ab\'elienne de la forme $\mathbb{G}_m^n \times A$},
  author = {Arnaud Plessis},
  journal= {arXiv preprint arXiv:1901.07980},
  year   = {2022}
}

Comments

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