Survey on the geometric Bogomolov conjecture
Publications mathématiques de Besançon. Algèbre et théorie des nombres (2017), pp. 137-193.

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.

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.

Published online:
DOI: 10.5802/pmb.19
Classification: 14G40, 11G50
Keywords: Geometric Bogomolov conjecture, Bogomolov conjecture, canonical heights, canonical measures, small points
Yamaki, Kazuhiko 1

1 Institute for Liberal Arts and Sciences, Kyoto University, Kyoto, 606-8501, Japan
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Yamaki, Kazuhiko. Survey on the geometric Bogomolov conjecture. Publications mathématiques de Besançon. Algèbre et théorie des nombres (2017), pp. 137-193. doi : 10.5802/pmb.19. http://archive.numdam.org/articles/10.5802/pmb.19/

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