Abstract
Let (R,m) be a complete local ring, a an ideal of R and N and L two Matlis reflexive R-modules with Supp(L) ⊆ V(a). We prove that if M is a finitely generated R-module, then Exti i R (L, H j a (M,N)) is Matlis reflexive for all i and j in the following cases:
-
(a)
dim R/a = 1
-
(b)
cd(a) = 1; where cd is the cohomological dimension of a in R
-
(c)
dim R ⩽ 2.
In these cases we also prove that the Bass numbers of H j a (M, N) are finite.
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This work was partially supported by the grant from IPM (No. 87130024).
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Mafi, A. Matlis reflexive and generalized local cohomology modules. Czech Math J 59, 1095–1102 (2009). https://doi.org/10.1007/s10587-009-0077-4
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DOI: https://doi.org/10.1007/s10587-009-0077-4