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

Abstract

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.

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

References in corpus (1)

• The spectrum of prime ideals in tensor triangulated categories

Cited by in corpus (5)

• Thick tensor ideals of right bounded derived categories
• A note on thick subcategories of stable derived categories
• The dimension of a subcategory of modules
• Singularity categories via the derived quotient
• Classification of resolving subcategories and grade consistent functions