In mathematics, a Frobenius splitting, introduced by , is a splitting of the injective morphism O<sub>X</sub>âÂÂF<sub>*</sub>O<sub>X</sub> from a structure sheaf O<sub>X</sub> of a characteristic p > 0 variety X to its image F<sub>*</sub>O<sub>X</sub> under the Frobenius endomorphism F<sub>*</sub>.
give a detailed discussion of Frobenius splittings.
A fundamental property of Frobenius-split projective schemes X is that the higher cohomology H<sup>i</sup>(X,L) (i > 0) of ample line bundles L vanishes.