The Bogomolov conjecture for totally degenerate abelian varieties

• 成果类型: Article
• 署名作者: Gubler, Walter
• 署名单位: Dortmund University of Technology
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-007-0049-y
• 发表日期: 2007
• 页码: 377-400
• 关键词: rigid geometry; points; CURVES; equidistribution; heights

摘要

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.