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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2018: 1.55

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Volume 2006, Issue 590


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

Hugues Randriambololona
Published Online: 2006-04-27 | DOI: https://doi.org/10.1515/CRELLE.2006.004


The aim of this paper is twofold. First we prove a theorem of extension of sections of a coherent subquotient of a metrized 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 metrized 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.

About the article

1Ecole nationale supérieure des télécommunications, 46, rue Barrault, 75634 Paris Cedex 13, France

Received: 2004-03-23

Revised: 2005-01-11

Published Online: 2006-04-27

Published in Print: 2006-01-26

Citation Information: Journal fur die reine und angewandte Mathematik (Crelles Journal), Volume 2006, Issue 590, Pages 67–88, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/CRELLE.2006.004.

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