Classification of categorical subspaces of locally noetherian schemes

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.

47 pages

References in corpus (3)

• Specialization orders on atom spectra of Grothendieck categories
• Extension groups between atoms and objects in locally noetherian Grothendieck category
• Rosenberg's Reconstruction Theorem (after Gabber)

Cited by in corpus (5)

• Finiteness of the number of minimal atoms in Grothendieck categories
• Extension groups between atoms in abelian categories
• Construction of Grothendieck categories with enough compressible objects using colored quivers
• Classifying subcategories, local algebra and the Rosenberg spectrum of a locally noetherian category
• On localizing subcategories of derived categories of categories of quasi-coherent sheaves on Noetherian algebraic spaces