Filter regular sequences and endomorphisms of local cohomology modules

Abstract

Let [Formula: see text] be a commutative Noetherian ring and [Formula: see text] be an ideal of [Formula: see text] such that [Formula: see text], where [Formula: see text] is the cohomological dimension of [Formula: see text] with respect to [Formula: see text] and [Formula: see text] is the grade of [Formula: see text]. We show that whenever, [Formula: see text] for all [Formula: see text] and all integers [Formula: see text] with [Formula: see text] and [Formula: see text], then there exists an exact sequence [Formula: see text] of endomorphisms of local cohomology modules, where [Formula: see text] and, for [Formula: see text], [Formula: see text] is the ring of fractions of [Formula: see text] with respect to multiplicatively closed subset [Formula: see text] of [Formula: see text].