Uniform annihilation of local cohomology and of Koszul homology

Abstract

Let R be a ring (all rings considered here are commutative with identity and Noetherian), M a finitely generated R-module, and I an ideal of R. The jth local cohomology module of M with support in I is defined byIn this paper, we prove a uniform version of a theorem of Brodmann about annihilation of local cohomology modules. As a corollary of this, we deduce a generalization of a theorem of Hochster and Huneke about uniform annihilation of Koszul homology.