Resumen de Vanishing, Bass numbers, and cominimaxness of local cohomology modules

Jafar A'zami

• Let (R,m) be a commutative Noetherian regular local ring and I be a proper ideal of R. It is shown that Hd−1p(R)=0 for any prime ideal p of R with dim(R/p)=2, whenever the set {n∈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 HiI(M) are finite, for all integers i≥0, whenever height(I)=1 or d≤3.