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Introduction to arithmetic Hilbert-Samuel theorems. (Introduction aux théorèmes de Hilbert-Samuel arithmétiques.) (French) Zbl 1458.14033

Peyre, Emmanuel (ed.) et al., Arakelov geometry and diophantine applications. Based on lectures given at the summer school, Grenoble, France, June 12–30, 2017. Cham: Springer. Lect. Notes Math. 2276, 77-103 (2021).
Summary: Le 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.
For the entire collection see [Zbl 1461.14005].

MSC:

14G40 Arithmetic varieties and schemes; Arakelov theory; heights
14-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry
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