Tilting and cluster tilting for quotient singularities

Details Tilting and cluster tilting for quotient singularities Tilting and cluster tilting for quotient singularities

2010-12-29

arxiv.org/abs/1012.5954v2

Mathematics

Representation Theory

31 pages

Scientific paper

We shall show that the stable categories of graded Cohen-Macaulay modules over quotient singularities have tilting objects. In particular, these categories are triangle equivalent to derived categories of finite dimensional algebras. Our method is based on higher dimensional Auslander-Reiten theory, which gives cluster tilting objects in the stable categories of (ungraded) Cohen-Macaulay modules.

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