Cofiniteness of generalized local cohomology modules

Abstract

Let [Formula: see text] be an ideal of a commutative noetherian ring [Formula: see text] and [Formula: see text] two [Formula: see text]-modules with [Formula: see text] finitely generated. It is shown that if either [Formula: see text] is an [Formula: see text]-cofinite module of dimension [Formula: see text] for all [Formula: see text], or [Formula: see text] is a principal ideal and [Formula: see text] is finitely generated for all [Formula: see text], or [Formula: see text] is finitely generated and [Formula: see text] for all [Formula: see text], then the [Formula: see text]-module [Formula: see text] is [Formula: see text]-cofinite for all [Formula: see text].