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Arakelov Geometry and Diophantine Applications pp 299–328Cite as

Chapter VII: Arakelov Geometry, Heights, Equidistribution, and the Bogomolov Conjecture

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2276))

Abstract

This text is an introduction to the theory of heights in Arakelov geometry, with emphasis on equidistribution theorems, their limit measures (in archimedean and non-archimedean contexts), and its application to Ullmo–Zhang’s proof of the Bogomolov conjecture.

To the memory of Lucien Szpiro

During the preparation of this paper, the author’s research was partially supported by ANR-13-BS01-0006 (Valcomo) and by ANR-15-CE40-0008 (Défigéo).

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Authors and Affiliations

  1. Université de Paris and Sorbonne Université, CNRS, IMJ-PRG, Paris, France

    Antoine Chambert-Loir

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  1. Antoine Chambert-Loir
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  1. Institut Fourier, Université Grenoble Alpes, Grenoble, France

    Emmanuel Peyre

  2. Institut Fourier, Université Grenoble Alpes, Grenoble, France

    Gaël Rémond

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Chambert-Loir, A. (2021). Chapter VII: Arakelov Geometry, Heights, Equidistribution, and the Bogomolov Conjecture. In: Peyre, E., Rémond, G. (eds) Arakelov Geometry and Diophantine Applications. Lecture Notes in Mathematics, vol 2276. Springer, Cham. https://doi.org/10.1007/978-3-030-57559-5_8

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