Survey on the geometric Bogomolov conjecture

Abstract

This is a survey paper of the developments on the geometric Bogomolov conjecture. We explain the recent results by the author as well as previous works concerning the conjecture. This paper also includes an introduction to the height theory over function fields and a quick review on basic notions on non-archimedean analytic geometry.

57 pages. This is an expanded lecture note of a talk at "Non-archimedean analytic Geometry: Theory and Practice" (24--28 August, 2015). It has been submitted to the conference proceedings. Appendix added

References in corpus (2)

• Non-density of small points on divisors on abelian varieties and the Bogomolov conjecture
• Geometric Bogomolov conjecture for nowhere degenerate abelian varieties of dimension $5$ with trivial trace

Cited by in corpus (1)

• The geometric Bogomolov conjecture