Cohomologically Cofinite Complexes

TL;DR

This paper advances the understanding of derived dic completion and torsion functors over noetherian rings, providing structural characterizations and a Nakayama theorem for cohomologically complete and cofinite complexes.

Contribution

It offers new structural characterizations and a Nakayama theorem for cohomologically complete and cofinite complexes over noetherian rings.

Findings

Structural characterization of bounded above cohomologically complete complexes

Cohomologically Complete Nakayama Theorem

Characterization of cohomologically cofinite complexes

Abstract

Let A be a commutative noetherian ring, and \a an ideal in it. In this paper we continue the study, begun in [PSY1], of the derived \a-adic completion and the derived \a-torsion functors. Here are our results: (1) a structural characterization of bounded above cohomologically complete complexes; (2) the Cohomologically Complete Nakayama Theorem; and (3) a characterization of cohomologically cofinite complexes.