The Bogomolov conjecture for totally degenerate abelian varieties
Number Theory
2009-11-11 v2 Algebraic Geometry
Abstract
We prove the Bogomolov conjecture for an abelian variety A over a function field which is totally degenerate at a place v. We adapt Zhang's proof of the number field case replacing the complex analytic tools by tropical analytic geometry. A key step is the tropical equidistribution theorem for A at the totally degenerate place. As an application, we obtain finiteness of torsion points with coordinates in the maximal unramified algebraic extension over v.
Keywords
Cite
@article{arxiv.math/0609387,
title = {The Bogomolov conjecture for totally degenerate abelian varieties},
author = {Walter Gubler},
journal= {arXiv preprint arXiv:math/0609387},
year = {2009}
}
Comments
21 pages; submitted. Minor errors corrected, applications in Section 6 added