THE FROBENIUS MORPHISM ON A TORIC VARIETY

We give a characteristic p proof of the Bott vanishing theorem for pro jective toric varieties using that the Frobenius morphism on a toric v ariety lifts to characteristic p(2). A proof of the Bott vanishing the orem was previously known only in the simplicial case. We also general ize the work of Paranjape and Srinivas about non-liftability to charac teristic zero of the Frobenius morphism on flag varieties by showing t hat Bott vanishing fails for a large class of flag varieties not isomo rphic to a product of projective spaces.