The Bogomolov conjecture for totally degenerate abelian varieties

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.

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

References in corpus (2)

• The Bogomolov conjecture for totally degenerate abelian varieties
• Tropical varieties for non-archimedean analytic spaces

Cited by in corpus (6)

• The Bogomolov conjecture for totally degenerate abelian varieties
• Tropical varieties for non-archimedean analytic spaces
• The Geometric Bogomolov Conjecture for Small Genus Curves
• Gross--Schoen Cycles and Dualising Sheaves
• Equidistribution over function fields
• Zhang's Conjecture and the Effective Bogomolov Conjecture over function fields