  Duality properties are studied for a Gorenstein algebra that is finite and
projective over its center. Using the homotopy category of injective modules,
it is proved that there is a local duality theorem for the subcategory of
acyclic complexes of such an algebra, akin to the local duality theorems of
Grothendieck and Serre in the context of commutative algebra and algebraic
geometry. A key ingredient is the Nakayama functor on the bounded derived
category of a Gorenstein algebra, and its extension to the full homotopy
category of injective modules.
