Another version of cosupport for complexes

TL;DR

This paper develops new versions of cosupport in the derived category of a ring, providing properties, examples, and comparisons to existing notions to deepen the understanding of cosupport theory.

Contribution

Introduces alternative definitions of big and small cosupport for complexes, expanding the theoretical framework and comparing with previous cosupport concepts.

Findings

New definitions of cosupport differ from previous versions.

Properties of cosupport are established and shown to be dual to support.

Examples illustrate differences and relations between big and small cosupport.

Abstract

The goal of the article is to get a satisfactory theory of cosupport in the derived category $\mathrm{D}(R)$, this is done by introducing another versions of the "big" and "small" cosupport for complexes. We provide some properties for cosupport that are similar--or rather dual--to those of support for complexes. By examples we show that these versions are differ from the cosupport in [J. Reine Angew. Math. 673 (2012) 161--207]. We also study some relations between the "big" and "small" cosupport and give some computations and comparisons of the "small" support and "small" cosupport.