Journal Article On the Auslander-Reiten conjecture for Cohen-Macaulay local rings

Goto, Shiro  ,  Takahashi, Ryo

145 ( 8 )  , pp.3289 - 3296 , 2017-08 , American Mathematical Society
This paper studies vanishing of Ext modules over Cohen-Macaulay local rings. The main result of this paper implies that the Auslander-Reiten conjecture holds for maximal Cohen-Macaulay modules of rank one overCohen-Macaulay normal local rings. It also recovers a theorem of Avramov-Buchweitz-Şega and Hanes-Huneke, which shows that the Tachikawa conjecture holds for Cohen-Macaulay generically Gorenstein local rings.

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