I know that if $R$ is Noetherian local with a finite module of finite injective dimension, then $R$ is Cohen-Macaulay.
Can one add assumptions on $M$, so that $R$ be Gorenstein or Complete intersection or Regular?
thank you.
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Sign up to join this communityI know that if $R$ is Noetherian local with a finite module of finite injective dimension, then $R$ is Cohen-Macaulay.
Can one add assumptions on $M$, so that $R$ be Gorenstein or Complete intersection or Regular?
thank you.
If you admit $M$ cyclic as additional assumtion, then $R$ is Gorenstein by a theorem in Peskine-Szpiro paper "Dimension projective finie et cohomologie locale", Theorem II.5.5.
To complete Vinteuil's answer:
You can find translation of "Local cohomology and finite projective dimension", by C. Peskine and L. Szpiro, here. (Translator is Srikanth B. Iyengar).