@article{oai:nagoya.repo.nii.ac.jp:00024751, author = {Goto, Shiro and Takahashi, Ryo}, issue = {8}, journal = {Proceedings of the American Mathematical Society}, month = {Aug}, note = {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 over Cohen-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.}, pages = {3289--3296}, title = {On the Auslander-Reiten conjecture for Cohen-Macaulay local rings}, volume = {145}, year = {2017} }