Cofiniteness of Generalized Local Cohomology Modules for One-Dimensional Ideals

Abstract

Abstract. Let a be an ideal of a commutative Noetherian ring R and M and N two finitely generated R-modules. Our main result asserts that if dim R/a ≤ 1, then all generalized local cohomology modules H i a (M, N) are a-cofinite.

Artinianness of Local Cohomology Modules

“…In particular, the Artinianness, cofiniteness and vanishing of local cohomology and generalized local cohomology modules are of special interests and several papers are devoted to study these problems where M and N are finitely generated R-modules (see [2], [5], [8], [9], [14], [18] and [23]). Recall that an R-module M is said to be I-cofinite if Supp R (M ) ⊆ V (I) and Ext j R (R/I, M ) is finitely generated for all j (see [13]).…”