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Tilting and cluster tilting for quotient singularities (1012.5954v2)
Published 29 Dec 2010 in math.RT, math.AC, and math.AG
Abstract: 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.