Classifying subcategories of modules
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Publication:2716134
DOI10.1090/S0002-9947-01-02747-7zbMATH Open0981.13006arXivmath/9912221MaRDI QIDQ2716134
Author name not available (Why is that?)
Publication date: 6 June 2001
Published in: (Search for Journal in Brave)
Abstract: In this paper, we classify certain subcategories of modules over a ring R. A wide subcategory of R-modules is an Abelian subcategory of R-Mod that is closed under extensions. We give a complete classification of wide subcategories of finitely presented modules when R is a quotient of a regular commutative coherent ring by a finitely generated ideal. This includes all finitely presented algebras over a principal ideal domain, as well as polynomial rings on infinitely many variable over a PID. The classification is in terms of subsets of Spec R, and depends heavily on Thomason's classification of thick subcategories of small objects in the derived category. We also classify all wide subcategories closed under arbitrary coproducts for any Noetherian commutative ring R. These correspond to arbitrary subsets of Spec R, and this classification depends on Neeman's classification of localizing subcategories of the derived category.
Full work available at URL: https://arxiv.org/abs/math/9912221
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