Survey on the geometric Bogomolov conjecture

Yamaki, Kazuhiko

Publications mathématiques de Besançon. Algèbre et théorie des nombres (2017), pp. 137-193.

Ce texte est un article de synthèse portant sur la conjecture de Bogomolov géométrique. Nous y expliquons nos résultats récents ainsi que les travaux qui les ont précédés. Cet article contient également une introduction à la théorie des hauteurs sur les corps de fonctions et un exposé rapide des notions de base de géométrique analytique non-archimédienne.

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 nonarchimedean analytic geometry.

Classification : 14G40, 11G50
Mots-clés : Geometric Bogomolov conjecture, Bogomolov conjecture, canonical heights, canonical measures, small points

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