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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Vanishing of cohomology over Gorenstein rings of small codimension


Author: Liana M. Sega
Journal: Proc. Amer. Math. Soc. 131 (2003), 2313-2323
MSC (2000): Primary 13D07, 13H10; Secondary 13D40
Published electronically: November 14, 2002
MathSciNet review: 1974627
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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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Additional Information

Liana M. Sega
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Address at time of publication: Mathematical Sciences Research Institute, 1000 Centennial Drive, Berkeley, California 94720
Email: lmsega@math.purdue.edu, lsega@msri.org

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06788-6
PII: S 0002-9939(02)06788-6
Keywords: Gorenstein rings, vanishing of Ext, CI-dimension
Received by editor(s): November 6, 2001
Received by editor(s) in revised form: March 5, 2002
Published electronically: November 14, 2002
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 2002 American Mathematical Society