Weights in the cohomology of toric varieties

We describe the weight filtration in the cohomology of toric varieties. We present a role of the Frobenius automorphism in an elementary way. We prove that equivariant intersection homology of an arbitrary toric variety is pure. We obtain results concerning Koszul duality: nonequivariant intersection cohomology is equal to the cohomology of the Koszul complex $IH_T^(X)\otimes H^(T)$\mathrm{.}Wealsodescribetheweightfiltrationin$IH^*(X)$.