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.