Derived category of equivariant coherent sheaves on a smooth toric variety and Koszul duality

Let X be a smooth toric variety defined by the fan {Σ} . We consider {Σ} as a finite set with topology and define a natural sheaf of graded algebras AΣ on {Σ} . The category of modules over AΣ is studied (together with other related categories). This leads to a certain combinatorial Koszul duality equivalence. We describe the equivariant category of coherent sheaves cohX,T and a related (slightly bigger) equivariant category OX,T-mod in terms of sheaves of modules over the sheaf of algebras AΣ . Eventually (for a complete X ) the combinatorial Koszul duality is interpreted in terms of the Serre functor on D^b(cohX,T)