Local-global principle for annihilation of general local cohomology

Abstract

Let A be a Noetherian ring, let M be a finitely generated A-module and let φ be a system of ideals of A. We prove that, for any ideal a in φ, if, for every prime ideal p of A, there exists an integer k(p), depending on p, such that ak(p) kills the general local cohomology module Hjφ (Mp) for every integer j less than a fixed integer n, where φp := {ap : a ε φ}, then there exists an integer k such that akHjφ(M) = 0 for every j < n. © 2001, Instytut Matematyczny. All rights reserved.