A finite result for the set of associated prime ideals of formal local cohomology modules

Abstract

Let [Formula: see text] be a Noetherian local ring, [Formula: see text] two ideals of [Formula: see text], and [Formula: see text] two finitely generated [Formula: see text]-modules. It is first shown that [Formula: see text] is a finite set. We also prove that except the maximal ideal [Formula: see text], the set [Formula: see text] is stable for large [Formula: see text], where we use [Formula: see text] to denote [Formula: see text]-module [Formula: see text] or [Formula: see text] and [Formula: see text] is the eventual value of [Formula: see text].