On the category of cofinite complexes and modules

TL;DR

This paper extends Hartshorne's work on cofinite complexes to broader classes of rings, explores conditions for an open question, and examines cofiniteness in lower-dimensional rings.

Contribution

It generalizes Hartshorne's characterization of cofinite complexes and provides new conditions for the affirmative resolution of a longstanding question.

Findings

Extended cofinite complex characterization to more general rings

Identified conditions for Hartshorne's fourth question to be answered affirmatively

Analyzed cofiniteness of complexes in lower-dimensional rings

Abstract

Let $A$ be a commutative noetherian ring, let $\mathfrak a$ be an ideal of $A$. In this paper, we extend Hartshorne's characterization of cofinite complexes to more general classes of rings. We also determine conditions under which Hartshorne's fourth question [H1] admits an affirmative answer. Finally, we investigate the cofiniteness of complexes of $\frak a$-cofinite modules for rings of lower dimensions.