Cofiniteness of top local cohomology modules.

Let R be a commutative Noetherian ring with non-zero identity, a an ideal of R, M a finitely generated R-module with finite Krull dimension d, and n a non-negative integer. In this paper, we prove that the top local cohomology module H a d - n (M) is an (FD < n , a) -cofinite R-module and { p ∈ Ass R (H a d - n (M)) : dim (R / p) ≥ n } is a finite set. As a consequence, we observe that Supp R (H a d - 1 (M)) is a finite set when R is a semi-local ring. [ABSTRACT FROM AUTHOR]