ON THE LOCAL COHOMOLOGY OF MINIMAX MODULES

Abstract

Let R be a commutative Noetherian ring, a an ideal of R, and M a minimax R-module. We prove that the local cohomology modules <TEX>$H^j_a(M)$</TEX> are a-cominimax; that is, <TEX>$Ext^i_R$</TEX>(R/a, <TEX>$H^j_a(M)$</TEX>) is minimax 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 <TEX>$R{\leq}2$</TEX>. In these cases we also prove that the Bass numbers and the Betti numbers of <TEX>$H^j_a(M)$</TEX> are finite.