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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
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
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
Linking options:
https://www.mathnet.ru/eng/aa1141 https://www.mathnet.ru/eng/aa/v21/i3/p93
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