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arXiv:math/0609387 [math.NT]AbstractReferencesReviewsResources

The Bogomolov conjecture for totally degenerate abelian varieties

Walter Gubler

Published 2006-09-14, updated 2007-02-06Version 2

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.

Comments: 21 pages; submitted. Minor errors corrected, applications in Section 6 added
Journal: Invent. Math. 169, No.2, 377-400 (2007)
Categories: math.NT, math.AG
Subjects: 14G40, 11G10
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