Titlebook: Arakelov Geometry and Diophantine Applications; Emmanuel Peyre,Ga?l Rémond Book 2021 The Editor(s) (if applicable) and The Author(s), unde

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Chapter III : Introduction aux théorèmes de Hilbert-Samuel arithmétiquesLe but de ce chapitre est d’expliquer quelques théorèmes de type Hilbert-Samuel, qui étudient le comportement asymptotique d’un système linéaire gradué éventuellement métrisé, dans différents contextes : géométrie algébrique, géométrie analytique et géométrie arithmétique.

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Chapter VII: Arakelov Geometry, Heights, Equidistribution, and the Bogomolov ConjectureThis 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.

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0075-8434 this popular and active area of research.Features well-writ.Bridging the gap between novice and expert, the aim of this book is to present in a self-contained way a number of striking examples of current diophantine problems to which Arakelov geometry has been or may be applied. Arakelov geometry c

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