VANISHING, BASS NUMBERS, AND COMINIMAXNESS OF LOCAL COHOMOLOGY MODULES

Let (R, m) be a commutative Noetherian regular local ring and I be a proper ideal of R. It is shown that H-p(d-1)(R) = 0 for any prime ideal p of R with dim(R/p) = 2, whenever the set {n is an element of N : R/p((n)) is Cohen-Macaulay} is infinite. Now, let (R, m) be a commutative Noetherian unique factorization local domain of dimension d, I an ideal of R, and M a finitely generated R-module. It is shown that the Bass numbers of the R-module H-I(i) (M) are finite, for all integers i >= 0, whenever height(I) = 1 or d <= 3.