  It is proved that for a commutative noetherian ring with dualizing complex
the homotopy category of projective modules is equivalent, as a triangulated
category, to the homotopy category of injective modules. Restricted to compact
objects, this statement is a reinterpretation of Grothendieck's duality
theorem. Using this equivalence it is proved that the (Verdier) quotient of the
category of acyclic complexes of projectives by its subcategory of totally
acyclic complexes and the corresponding category consisting of injective
modules are equivalent. A new characterization is provided for complexes in
Auslander categories and in Bass categories of such rings.
