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Arithmetic Hilbert-Samuel theorem. (Théorème de Hilbert-Samuel arithmétique.) (French) Zbl 0818.14011

Summary: We give a new direct proof of the arithmetic Hilbert-Samuel theorem from which we deduce a criterion for the existence of sections of an ample line bundle over an arithmetic variety with sup norm less than one.

MSC:

14G40 Arithmetic varieties and schemes; Arakelov theory; heights
32L10 Sheaves and cohomology of sections of holomorphic vector bundles, general results
13D40 Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series
11G99 Arithmetic algebraic geometry (Diophantine geometry)
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