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 letbe a system of ideals of A. We prove that, for any ideal a in �, if, for every prime ideal p of A, there exists an integer k(p), depending on p, such that a k(p) kills the general local cohomology module H j �p (Mp) for every integer j less than a fixed integer n, where �p :={ap : a2 �}, then there exists an integer k such that a k H j (M) = 0 for every j < n.