Abstract

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Representation theory of CM (=Cohen-Macaulay) modules were initiated by 

<br>
Auslander-Reiten. The stable categories of CM modules were recently studied 

<br>
by many people as singular derived categories (Goresntein case) and as stable 

<br>
categories of matrix factorizations (hypersurface case). I will explain their 

<br>
properties in the context of tilting theory as well as cluster tilting theory. 

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In particular we will see that the stable categories of graded (resp. ungraded)

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CM modules are often realized as derived (resp. cluster) categories of certain 

<br>
algebras by using tilting (resp. cluster tilting) theory.