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

Gillet, Henri; Soulé, Christophe

C. R. Acad. Sci., Paris, Sér. I 307, No. 17, 887-890 (1988).

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

MSC:

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

Keywords:

arithmetic variety; number of sections of a Hermitian vector bundle