A generalization of the cofiniteness problem in local cohomology modules

Abstract

Let R be a commutative Noetherian ring with nonzero identity and let M be a finitely generated R-module. In this paper, we prove that if an ideal I of R is generated by a u.s.d-sequence on M then the local cohomology module H Ii(M) is I-cofinite. Furthermore, for any system of ideals φ of R, we study the cofiniteness problem in the context of general local cohomology modules.