A generalization of the cofiniteness problem in local cohomology modules

Abstract

AbstractLetRbe a commutative Noetherian ring with nonzero identity and letMbe a finitely generated R-module. In this paper, we prove that if an idealIofRis generated by a u.s.d-sequence onMthen the local cohomology module(M) isI-cofinite. Furthermore, for any system of ideals Φ of R, we study the cofiniteness problem in the context of general local cohomology modules.