Frobenius splitting

In mathematics, a Frobenius splitting, introduced by , is a splitting of the injective morphism O"X"→F*O"X" from a structure sheaf O"X" of a characteristic "p" > 0 variety "X" to its image F*O"X" 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 "H""i"("X","L") ("i" > 0) of ample line bundles "L" vanishes.