  Let (X;OX) be a locally noetherian scheme with a dualizing complex D. We
prove that DOX - : K(PinfX)----> K(InjX) is an equivalence of triangulated
categories where K(InjX) is the homotopy category of injective quasi-coherent
OX- modules and K(PinfX) is the homotopy category of pure injective flat
quasi-coherent OX-modules. Where X is affine, we show that this equivalence is
the infinite completion of the Grothendieck duality theorem. Furthermore, we
prove that D OX - induces an equivalence between the pure derived category of
flats and the pure derived category of absolutely pure quasi-coherent
OX-modules.
