Cotilting Modules and Gorenstein Homological Dimensions

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 Noetherian rings.