Métriques de sous-quotient et théorème de Hilbert-Samuel arithmétique pour les faisceaux cohérents
Identifieur interne : 000E49 ( Istex/Corpus ); précédent : 000E48; suivant : 000E50Métriques de sous-quotient et théorème de Hilbert-Samuel arithmétique pour les faisceaux cohérents
Auteurs : Hugues RandriambololonaSource :
- 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
Links to Exploration step
ISTEX:46E7DE14DCC0D507B62774FE61E7F126EA9DAB9CLe document en format XML
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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.</p></abstract></profileDesc><revisionDesc><change when="2006-04-27">Created</change><change when="2006-01-26">Published</change><change xml:id="refBibs-istex" who="#ISTEX-API" when="2017-10-5">References added</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/46E7DE14DCC0D507B62774FE61E7F126EA9DAB9C/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="corpus degruyter-journals" wicri:toSee="no header"><istex:xmlDeclaration>version="1.0" encoding="UTF-8"</istex:xmlDeclaration><istex:docType PUBLIC="-//Atypon//DTD Atypon Systems Archival NLM DTD Suite v2.2.0 20090301//EN" URI="nlm-dtd/archivearticle.dtd" name="istex:docType"></istex:docType><istex:document><article article-type="research-article" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">crll</journal-id><abbrev-journal-title abbrev-type="full">Journal fur die reine und angewandte Mathematik (Crelles Journal)</abbrev-journal-title><issn pub-type="ppub">0075-4102</issn><issn pub-type="epub">1435-5345</issn><publisher><publisher-name>Walter de Gruyter</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">crll.2006.590.67</article-id><article-id pub-id-type="doi">10.1515/CRELLE.2006.004</article-id><title-group><article-title>Métriques de sous-quotient et théorème de Hilbert-Samuel arithmétique pour les faisceaux cohérents</article-title></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name><given-names>Hugues</given-names><x> </x><surname>Randriambololona</surname></name><xref ref-type="aff" rid="a1"><sup>1</sup></xref><xref ref-type="corresp" rid="cor1"><sup>1</sup></xref><aff id="a1"><label><sup>1</sup></label>Paris.</aff><email xlink:href="mailto:randriam@enst.fr">randriam@enst.fr</email></contrib></contrib-group><author-notes><corresp id="cor1"><sup>1</sup><addr-line>Ecole nationale supérieure des télécommunications, 46, rue Barrault, 75634 Paris Cedex 13, France</addr-line></corresp></author-notes><pub-date pub-type="ppub"><day>26</day><month>01</month><year>2006</year><string-date>January 2006</string-date></pub-date><pub-date pub-type="epub"><day>27</day><month>04</month><year>2006</year></pub-date><volume>2006</volume><issue>590</issue><fpage>67</fpage><lpage>88</lpage><history><date date-type="received"><day>23</day><month>03</month><year>2004</year></date><date date-type="rev-recd"><day>11</day><month>01</month><year>2005</year></date></history><copyright-statement>© Walter de Gruyter</copyright-statement><copyright-year>2006</copyright-year><related-article related-article-type="pdf" xlink:href="crelle.2006.004.pdf"></related-article><abstract><title>Abstract</title><p>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.</p></abstract></article-meta></front></article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Métriques de sous-quotient et théorème de Hilbert-Samuel arithmétique pour les faisceaux cohérents</title></titleInfo><titleInfo type="alternative" lang="en" contentType="CDATA"><title>Métriques de sous-quotient et théorème de Hilbert-Samuel arithmétique pour les faisceaux cohérents</title></titleInfo><name type="personal"><namePart type="given">Hugues</namePart><namePart type="family">Randriambololona</namePart><affiliation>1 Paris.</affiliation><affiliation>Paris.</affiliation><affiliation>E-mail: randriam@enst.fr</affiliation></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="research-article" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-1JC4F85T-7">research-article</genre><originInfo><publisher>Walter de Gruyter</publisher><dateIssued encoding="w3cdtf">2006-01-26</dateIssued><dateCreated encoding="w3cdtf">2006-04-27</dateCreated><copyrightDate encoding="w3cdtf">2006</copyrightDate></originInfo><language><languageTerm type="code" authority="iso639-2b">eng</languageTerm><languageTerm type="code" authority="rfc3066">en</languageTerm></language><abstract 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.</abstract><note type="author-notes">1 Ecole nationale supérieure des télécommunications, 46, rue Barrault, 75634 Paris Cedex 13, France</note><relatedItem type="host"><titleInfo><title>Journal fur die reine und angewandte Mathematik (Crelles Journal)</title></titleInfo><titleInfo type="abbreviated"><title>Journal fur die reine und angewandte Mathematik (Crelles Journal)</title></titleInfo><genre type="journal" authority="ISTEX" authorityURI="https://publication-type.data.istex.fr" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-0GLKJH51-B">journal</genre><originInfo></originInfo><identifier type="ISSN">0075-4102</identifier><identifier type="eISSN">1435-5345</identifier><identifier type="PublisherID">crll</identifier><part><date>2006</date><detail type="volume"><caption>vol.</caption><number>2006</number></detail><detail type="issue"><caption>no.</caption><number>590</number></detail><extent unit="pages"><start>67</start><end>88</end></extent></part></relatedItem><identifier type="istex">46E7DE14DCC0D507B62774FE61E7F126EA9DAB9C</identifier><identifier type="ark">ark:/67375/QT4-MCGMZZZB-2</identifier><identifier type="DOI">10.1515/CRELLE.2006.004</identifier><identifier type="ArticleID">crll.2006.590.67</identifier><identifier type="pdf">crelle.2006.004.pdf</identifier><accessCondition type="use and reproduction" contentType="copyright">© Walter de Gruyter, 2006</accessCondition><recordInfo><recordContentSource authority="ISTEX" authorityURI="https://loaded-corpus.data.istex.fr" valueURI="https://loaded-corpus.data.istex.fr/ark:/67375/XBH-B4QPMMZB-D">degruyter-journals</recordContentSource><recordOrigin>© Walter de Gruyter</recordOrigin></recordInfo></mods><json:item><extension>json</extension><original>false</original><mimetype>application/json</mimetype><uri>https://api.istex.fr/document/46E7DE14DCC0D507B62774FE61E7F126EA9DAB9C/metadata/json</uri></json:item></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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