Cotilting modules and Gorenstein homological dimensions

TL;DR

This paper extends known characterizations of modules with finite Gorenstein homological dimensions from dualizing modules to cotilting modules over general Noetherian rings, broadening the theoretical framework.

Contribution

It provides an analogue of the Auslander and Bass class characterizations in the setting of cotilting modules over Noetherian rings, generalizing previous results.

Findings

Characterization of modules with finite Gorenstein flat dimension via cotilting modules

Characterization of modules with finite Gorenstein injective dimension via cotilting modules

Extension of classical duality results to a broader cotilting context

Abstract

For a dualizing module $D$ over a commutative Noetherian ring $R$ with identity, it is known that its Auslander class $\mathscr{A}_D\left(R\right)$ (respectively, Bass class $\mathscr{B}_D\left(R\right)$) is characterized as those $R$-modules with finite Gorenstein flat dimension (respectively, finite Gorenstein injective dimension). We establish an analogue of this result in the context of cotilting modules over general Noetherain rings.