Amplitude arithmétique. (Arithmetic ampleness). (French) Zbl 0676.14007

An asymptotic estimate for large n is given for the number of sections of a Hermitian vector bundle twisted n times with a Hermitian invertible line bundle, given over an arithmetic base variety, in particular showing the existence of a section of norm less than 1.
Reviewer: J.H.de Boer


14G99 Arithmetic problems in algebraic geometry; Diophantine geometry
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14C20 Divisors, linear systems, invertible sheaves