The Bogomolov conjecture for totally degenerate abelian varieties

• Autores: Walter Gubler
• Localización: Inventiones mathematicae, ISSN 0020-9910, Vol. 169, Nº. 2, 2007, págs. 377-400
• Idioma: inglés
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• Resumen

  • We prove the Bogomolov conjecture for a totally degenerate abelian variety A over a function field. 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 v. As a corollary, we obtain finiteness of torsion points with coordinates in the maximal unramified algebraic extension over v.