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arXiv · 1904.05630

Arakelov geometry, heights, equidistribution, and the Bogomolov conjecture

Antoine Chambert-Loir
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Abstract

This is an introduction to the topics of the title, from the 2017 Grenoble Summer school on Arakelov geometry and arithmetic applications. We review Arithmetic intersection numbers, explain the definition of the height of a variety and its properties, both in the framework of classical Arakelov geometry and of Zhang's adelic formalism. We then discuss arithmetic ampleness and its application to the equidistribution theorem of Szpiro-Ullmo-Zhang-Yuan, both at complex and nonarchimedean places. We conclude with Ullmo-Zhang's proof of the Bogomolov conjecture over number fields.

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Antoine Chambert-Loir. 2020-06-06. Arakelov geometry, heights, equidistribution, and the Bogomolov conjecture. https://doi.org/10.1007/978-3-030-57559-5_8

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