Vanishing of cohomology over Gorenstein rings of small codimension

Şega, Liana

doi:10.1090/S0002-9939-02-06788-6

Vanishing of cohomology over Gorenstein rings of small codimension
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by Liana M. Şega

Proc. Amer. Math. Soc. 131 (2003), 2313-2323

DOI: https://doi.org/10.1090/S0002-9939-02-06788-6

Published electronically: November 14, 2002

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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 $\operatorname {Ext}^n_R(M,N)$ for $n\gg 0$ is equivalent to the vanishing of $\operatorname {Ext}^n_R(N,M)$ for $n\gg 0$. Furthermore, if $\widehat {R}$ has no embedded deformation, then such vanishing occurs if and only if $M$ or $N$ has finite projective dimension.

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