Derived dualities induced by a 1-cotilting bimodule

TL;DR

This paper characterizes modules and complexes related to dualities from a 1-cotilting bimodule using linear compactness, extending classical reflexivity results and revealing finiteness properties of rings and modules.

Contribution

It generalizes the classical characterization of reflexive modules to dualities induced by 1-cotilting bimodules using a linear compactness condition.

Findings

Modules and complexes involved are characterized by linear compactness.

Finiteness properties of rings and modules are derived.

The work extends classical reflexivity characterizations.

Abstract

In this paper we characterize the modules and the complexes involved in the dualities induced by a 1-cotilting bimodule in terms of a linear compactness condition. Our result generalizes the classical characterization of reflexive modules with respect to Morita dualities. The linear compactness notion considered, permits us to obtain finiteness properties of the rings and modules involved.