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Vanishing of cohomology over Gorenstein rings of small codimension

Liana M Sega
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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 Ext^n_R(M,N) for n\gg 0 is equivalent to the vanishing of Ext^n_R(N,M) for n\gg 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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Liana M Sega. 2002-09-27. Vanishing of cohomology over Gorenstein rings of small codimension. https://arxiv.org/abs/math/0209389

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