Métriques de sous-quotient et théorème de Hilbert-Samuel arithmétique pour les faisceaux cohérents
Identifieur interne : 000E49 ( Istex/Curation ); précédent : 000E48; suivant : 000E50Métriques de sous-quotient et théorème de Hilbert-Samuel arithmétique pour les faisceaux cohérents
Auteurs : Hugues Randriambololona [France]Source :
- Journal fur die reine und angewandte Mathematik (Crelles Journal) [ 0075-4102 ] ; 2006-01-26.
English descriptors
- KwdEn :
- Ainsi, Analytique, Arithmetique, Aussi, Avec, Bres, Canonique, Cette, Coherents, Coker, Comme, Complexe, Compte tenu, Conjugaison complexe, Convergence, Convergence uniforme, Courbure, Courbure strictement, Degre, Donc, Donne, Donnee, Dont, Encore, Entier, Espace, Espace analytique complexe, Espaces, Etant, Exemple, Existe, Faisceau, Faisceaux, Ferme, Fonction, Forme, Formule, Hermitien, Inversible, Isomorphisme, Kskly, Libre, Localement, Ltration, Maintenant, Metrique, Metriques, Metrise, Module, Module inversible, Module localement libre metrise, Module norme, Modules coherents, Morphisme, Moyen, Muni, Muni structure, Naturelle, Naturellement, Norme, Normes, Normes uniformes, Notons, Peut, Plurisousharmonique, Preuve, Quotient, Randriambololona, Reduit, Reel, Relativement, Remarquons, Resp, Resultat, Soient, Soit, Sont, Sorte, Sou, Strictement, Strictement plurisousharmonique, Tels, Theoreme, Topologie, Topologie canonique, Uniforme, Vectoriel, Vectoriel muni structure.
- Teeft :
- Ainsi, Analytique, Arithmetique, Aussi, Avec, Bres, Canonique, Cette, Coherents, Coker, Comme, Complexe, Compte tenu, Conjugaison complexe, Convergence, Convergence uniforme, Courbure, Courbure strictement, Degre, Donc, Donne, Donnee, Dont, Encore, Entier, Espace, Espace analytique complexe, Espaces, Etant, Exemple, Existe, Faisceau, Faisceaux, Ferme, Fonction, Forme, Formule, Hermitien, Inversible, Isomorphisme, Kskly, Libre, Localement, Ltration, Maintenant, Metrique, Metriques, Metrise, Module, Module inversible, Module localement libre metrise, Module norme, Modules coherents, Morphisme, Moyen, Muni, Muni structure, Naturelle, Naturellement, Norme, Normes, Normes uniformes, Notons, Peut, Plurisousharmonique, Preuve, Quotient, Randriambololona, Reduit, Reel, Relativement, Remarquons, Resp, Resultat, Soient, Soit, Sont, Sorte, Sou, Strictement, Strictement plurisousharmonique, Tels, Theoreme, Topologie, Topologie canonique, Uniforme, Vectoriel, Vectoriel muni structure.
Abstract
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.
Url:
DOI: 10.1515/CRELLE.2006.004
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<front><div type="abstract" xml:lang="en">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.</div>
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