ON THE LOCAL COHOMOLOGY OF MINIMAX MODULES

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 H(a)(j)(M) are a-cominimax; that is, Ext(R)(i)(R/a, H(a)(j)(M)) 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 R <= 2. In these cases we also prove that the Bass numbers and the Betti numbers of H(a)(j)(M) are finite.