Classifying finite localizations of quasicoherent sheaves
Classifying finite localizations of quasicoherent sheaves
复制标题
对准相干滑轮的有限局域化进行分类
DOI：
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发表时间：
2007
期刊：
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通讯作者：
G. Garkusha
中科院分区：
文献类型：
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作者：
G. Garkusha
给定一个拟紧的拟分离概型X，得到Qcoh（X）中的张量局部化有限型子范畴与所有子集Y subseteq X的集合Y= Y的双射建立了igcup_{iinOmega}Y_i$，其中$Xsetminus Y_i$是拟紧的，且对所有$iinOmega$是开的.作为应用，构造了环空间（X，O_X）->（Spec（Qcoh（X）），O_{Qcoh（X）}）的同构，其中$（Spec（Qcoh（X）），O_{Qcoh（X）}）$是与张量局部化有限型子范畴格相联系的环空间.同时，建立了完备复形$perf（X）$的张量厚子范畴与Qcoh（X）中有限型张量局部化子范畴之间的双射对应.
Given a quasi-compact, quasi-separated scheme X, a bijection between the tensor localizing subcategories of finite type in Qcoh(X) and the set of all subsets $Ysubseteq X$ of the form $Y=igcup_{iinOmega}Y_i$, with $Xsetminus Y_i$ quasi-compact and open for all $iinOmega$, is established. As an application, there is constructed an isomorphism of ringed spaces (X,O_X)-->(Spec(Qcoh(X)),O_{Qcoh(X)}), where $(Spec(Qcoh(X)),O_{Qcoh(X)})$ is a ringed space associated to the lattice of tensor localizing subcategories of finite type. Also, a bijective correspondence between the tensor thick subcategories of perfect complexes $perf(X)$ and the tensor localizing subcategories of finite type in Qcoh(X) is established.