DOCUMENTA MATHEMATICA, Vol. 20 (2015), 1403-1465

Ryo Kanda

Classification of Categorical Subspaces of Locally Noetherian Schemes

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.

2010 Mathematics Subject Classification: 18F20 (Primary), 18E15, 16D90, 14A22, 13C05 (Secondary)

Keywords and Phrases: Locally noetherian scheme; prelocalizing subcategory; localizing subcategory; closed subcategory; local filter

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