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The Local Cohomology Modules of Matlis Reflexive Modules are Almost Cofinite

Richard Belshoff, Susan Palmer Slattery and Cameron Wickham
Proceedings of the American Mathematical Society
Vol. 124, No. 9 (Sep., 1996), pp. 2649-2654
Stable URL: http://www.jstor.org/stable/2161703
Page Count: 6
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
The Local Cohomology Modules of Matlis Reflexive Modules are Almost Cofinite
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Abstract

We show that if M and N are Matlis reflexive modules over a complete Gorenstein local domain R and I is an ideal of R such that the dimension of R/I is one, then the modules $\operatorname{Ext}^i_R(N, H^j_I(M))$ are Matlis reflexive for all i and j if $\operatorname{Supp}(N) \subseteq V(I)$. It follows that the Bass numbers of Hj I(M) are finite. If R is not a domain, then the same results hold for M = R.

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