Classifying finite localizations of quasi-coherent sheaves
Algebraic Geometry
2007-08-14 v1 K-Theory and Homology
Abstract
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 of the form , with quasi-compact and open for all , is established. As an application, there is constructed an isomorphism of ringed spaces (X,O_X)-->(Spec(Qcoh(X)),O_{Qcoh(X)}), where 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 and the tensor localizing subcategories of finite type in Qcoh(X) is established.
Keywords
Cite
@article{arxiv.0708.1622,
title = {Classifying finite localizations of quasi-coherent sheaves},
author = {Grigory Garkusha},
journal= {arXiv preprint arXiv:0708.1622},
year = {2007}
}