Vanishing of cohomology over Gorenstein rings of small codimension
Abstract
We prove that if M, N are finite modules over a Gorenstein local ring R of codimension at most 4, then the vanishing of ExtnR(M,N) for n 0 is equivalent to the vanishing of ExtnR(N,M) for n 0. Furthermore, if the completion of R has no embedded deformation, then such vanishing occurs if and only if M or N has finite projective dimension.
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