摘要翻译：
给出了一个拟紧拟分离格式X,建立了Qcoh(X)中有限型张量局部化子范畴与形式为$y=\bigcup_{i\in\omega}y_i$的所有子集的集合$y\subseteq X$之间的双射，其中$X\set减去y_i$拟紧且对所有$i\in\omega开。作为应用，构造了环空间(X，O_X)-->(Spec(Qcoh(X))，O_{Qcoh(X)}）的同构，其中$(Spec(Qcoh(X))，O_{Qcoh(X)})$是与有限类型张量局部化子范畴的格相关联的环空间。建立了完全复形的张量厚子范畴$\perf(X)$与Qcoh(X)中有限型张量局部化子范畴之间的双射对应关系。
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英文标题：
《Classifying finite localizations of quasi-coherent sheaves》
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作者：
Grigory Garkusha
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最新提交年份：
2007
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分类信息：

一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics        数学
二级分类：K-Theory and Homology        K-理论与同调
分类描述：Algebraic and topological K-theory, relations with topology, commutative algebra, and operator algebras
代数和拓扑K-理论，与拓扑的关系，交换代数和算子代数
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英文摘要：
  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 $Y\subseteq X$ of the form $Y=\bigcup_{i\in\Omega}Y_i$, with $X\setminus Y_i$ quasi-compact and open for all $i\in\Omega$, 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.
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PDF链接：
https://arxiv.org/pdf/0708.1622