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Algebra i Analiz, 2009, Volume 21, Issue 3, Pages 93–129 (Mi aa1141)  

This article is cited in 11 scientific papers (total in 11 papers)

Research Papers

Classifying finite localizations of quasi-coherent sheaves

G. A. Garkusha

Department of Mathematics, Swansea University, Swansea, United Kingdom
References:
Abstract: Given a quasicompact, quasiseparated scheme $X$, a bijection between the tensor localizing subcategories of finite type in $\operatorname{Qcoh}(X)$ and the set of all subsets $Y\subseteq X$ of the form $Y=\bigcup_{i\in\Omega}Y_i$, with $X\setminus Y_i$ quasicompact and open for all $i\in\Omega$, is established. As an application, an isomorphism of ringed spaces
$$ (X,\mathcal{O}_X)\overset{\cong}{\longrightarrow}(\sf{spec}(\operatorname{Qcoh}(X)),\mathcal{O}_{\operatorname{Qcoh}(X)}) $$
is constructed, where $(\sf{spec}(\operatorname{Qcoh}(X)),\mathcal{O}_{\operatorname{Qcoh}(X)})$ is a ringed space associated with the lattice of tensor localizing subcategories of finite type. Also, a bijective correspondence between the tensor thick subcategories of perfect complexes $\mathcal{D}_{\operatorname{per}}(X)$ and the tensor localizing subcategories of finite type in $\operatorname{Qcoh}(X)$ is established.
Received: 20.07.2008
English version:
St. Petersburg Mathematical Journal, 2010, Volume 21, Issue 3, Pages 433–458
DOI: https://doi.org/10.1090/S1061-0022-10-01102-7
Bibliographic databases:
Document Type: Article
MSC: 14A15, 18F20
Language: Russian
Citation: G. A. Garkusha, “Classifying finite localizations of quasi-coherent sheaves”, Algebra i Analiz, 21:3 (2009), 93–129; St. Petersburg Math. J., 21:3 (2010), 433–458
Citation in format AMSBIB
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\by G.~A.~Garkusha
\paper Classifying finite localizations of quasi-coherent sheaves
\jour Algebra i Analiz
\yr 2009
\vol 21
\issue 3
\pages 93--129
\mathnet{http://mi.mathnet.ru/aa1141}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2588764}
\zmath{https://zbmath.org/?q=an:1211.14008}
\transl
\jour St. Petersburg Math. J.
\yr 2010
\vol 21
\issue 3
\pages 433--458
\crossref{https://doi.org/10.1090/S1061-0022-10-01102-7}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000277451000004}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84871308495}
Linking options:
  • https://www.mathnet.ru/eng/aa1141
  • https://www.mathnet.ru/eng/aa/v21/i3/p93
  • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Алгебра и анализ St. Petersburg Mathematical Journal
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    References:37
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