Gillet, Henri; Soulé, Christophe Amplitude arithmétique. (Arithmetic ampleness). (French) Zbl 0676.14007 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 Cited in 3 ReviewsCited in 20 Documents 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 PDF BibTeX XML Cite \textit{H. Gillet} and \textit{C. Soulé}, C. R. Acad. Sci., Paris, Sér. I 307, No. 17, 887--890 (1988; Zbl 0676.14007) OpenURL