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

By Ryo Takahashi. 2009

124 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/514f469f18a56b3e1bb2531c9c8670388703c6d2

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Classification of resolving subcategories and grade consistent functions (2012, result): “For many other similar results, see [5, 17, 19, 21, 23] and the references therein.”
Subcategories of singularity categories via tensor actions (2011, result): “The first main result extends work of Takahashi [Tak10] who has classified thick subcategories of DSg(R) when R is a local hypersurface.”
Orlov spectra: bounds and gaps (2010, background): “Let us return to the case of a general isolated hypersurface singularity, see also [54] Section 5.”