# Vanishing of Ext, cluster tilting modules and finite global dimension of endomorphism rings

@article{Dao2010VanishingOE, title={Vanishing of Ext, cluster tilting modules and finite global dimension of endomorphism rings}, author={Hailong Dao and Craig Huneke}, journal={American Journal of Mathematics}, year={2010}, volume={135}, pages={561 - 578} }

Let $R$ be a Cohen-Macaulay ring and $M$ a maximal Cohen-Macaulay $R$-module. Inspired by recent striking work by Iyama, Burban-Iyama-Keller-Reiten and van den Bergh we study the question of when the endomorphism ring of $M$ has finite global dimension via certain conditions about vanishing of Ext modules. We are able to strengthen certain results by Iyama on connections between a higher dimension version of Auslander correspondence and existence of non-commutative crepant resolutions. We also…

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