Abstract
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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have