Classifying thick subcategories of the stable category of Cohen-Macaulay modules

Details Classifying thick subcategories of the stable category of Cohen-Macaulay modules Classifying thick subcategories of the stable category of Cohen-Macaulay modules

2009-08-02

arxiv.org/abs/0908.0107v3

Mathematics

Commutative Algebra

39 pages. Final version. To appear in Advances in Mathematics. The contents of Section 4 in the previous version will be inclu

Scientific paper

Various classification theorems of thick subcategories of a triangulated category have been obtained in many areas of mathematics. In this paper, as a higher-dimensional version of the classification theorem of thick subcategories of the stable category of finitely generated representations of a finite $p$-group due to Benson, Carlson and Rickard, we consider classifying thick subcategories of the stable category of Cohen-Macaulay modules over a Gorenstein local ring. The main result of this paper yields a complete classification of the thick subcategories of the stable category of Cohen-Macaulay modules over a local hypersurface in terms of specialization-closed subsets of the prime ideal spectrum of the ring which are contained in its singular locus.

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