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arXiv · 1405.4473

Classification of categorical subspaces of locally noetherian schemes

Ryo Kanda
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Abstract

We classify the prelocalizing subcategories of the category of quasi-coherent sheaves on a locally noetherian scheme. In order to give the classification, we introduce the notion of a local filter of subobjects of the structure sheaf. The essential part of the argument is given as results on a Grothendieck category with certain properties. We also classify the localizing subcategories, the closed subcategories, and the bilocalizing subcategories in terms of filters.

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Ryo Kanda. 2014-05-18. Classification of categorical subspaces of locally noetherian schemes. https://arxiv.org/abs/1405.4473

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