The local cohomology modules of Matlis reflexive modules are almost cofinite

Abstract

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