The Bogomolov conjecture for totally degenerate abelian varieties

Details The Bogomolov conjecture for totally degenerate abelian varieties The Bogomolov conjecture for totally degenerate abelian varieties

2006-09-14

arxiv.org/abs/math/0609387v2

Invent. Math. 169, No.2, 377-400 (2007)

Mathematics

Number Theory

21 pages; submitted. Minor errors corrected, applications in Section 6 added

Scientific paper

10.1007/s00222-007-0049-y

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.

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