Métriques de sous-quotient et théorème de Hilbert-Samuel arithmétique pour les faisceaux cohérents

Abstract : The aim of this paper is twofold. First we prove a theorem of extension of sections of a coherent subquotient of a hermitian vector bundle on a complex analytic space with control of the norms, without any of the smoothness assumptions that were needed in previously known analogous results. Then we show how to associate an arithmetic Hilbert-Samuel function to a coherent sheaf on an arithmetic variety -- provided this coherent sheaf is a subquotient of a hermitian vector bundle -- and using the classical arithmetic Hilbert-Samuel theorem and our extension theorem, we give the leading term of the so constructed arithmetic Hilbert-Samuel function.
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-00122198
Contributor : Import Arxiv <>
Submitted on : Thursday, December 28, 2006 - 8:45:18 AM
Last modification on : Thursday, October 17, 2019 - 12:33:44 PM

Links full text

Identifiers

Citation

Hugues Randriam. Métriques de sous-quotient et théorème de Hilbert-Samuel arithmétique pour les faisceaux cohérents. Journal für die Reine und Angewandte Mathematik, 2006, 590, pp.67-88. ⟨hal-00122198⟩

Share

Metrics

Record views

144