%0 Journal Article %T Non-commutative crepant resolutions %A Michel Van den Bergh %J Mathematics %D 2002 %I arXiv %X We introduce the notion of a ``non-commutative crepant'' resolution of a singularity and show that it exists in certain cases. We also give some evidence for an extension of a conjecture by Bondal and Orlov, stating that different crepant resolutions of a Gorenstein singularity have the same derived category. %U http://arxiv.org/abs/math/0211064v2