Survey on the geometric Bogomolov conjecture

TL;DR

This survey reviews recent progress on the geometric Bogomolov conjecture, covering height theory over function fields and non-archimedean geometry, highlighting key developments and the author's contributions.

Contribution

It provides a comprehensive overview of recent advances and the author's own results related to the geometric Bogomolov conjecture.

Findings

Summary of recent results on the conjecture

Introduction to height theory over function fields

Review of non-archimedean analytic geometry

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.