Frobenius splitting

In mathematics, a Frobenius splitting, introduced by, is a splitting of the injective morphism OX→F*OX from a structure sheaf OX of a characteristic p > 0 variety X to its image F*OX under the Frobenius endomorphism F*.

give a detailed discussion of Frobenius splittings.

A fundamental property of Frobenius-split projective schemes X is that the higher cohomology Hi(X,L) (i > 0) of ample line bundles L vanishes.