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}
}
  • H. DaoC. Huneke
  • Published 28 May 2010
  • Mathematics
  • American Journal of Mathematics
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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