Bass numbers of derived local cohomology with respect to a specialization closed subset

Abstract

Let [Formula: see text] be a specialization closed subset of Spec [Formula: see text] and [Formula: see text] a left homologically bounded complex with finitely generated homologies. We provide some inequalities between the Bass numbers of [Formula: see text] and its local cohomology modules with respect to [Formula: see text]. As an application of these inequalities, we provide a comparison between the injective dimensions of [Formula: see text] and its nonzero local cohomology module [Formula: see text]. Our versions contain variations of some results already known in these areas.