In algebraic geometry, a Frobenius splitting, introduced by Mehta and Ramanathan, is a splitting of the injective morphism from a structure sheaf of a characteristic variety to its image under the Frobenius endomorphism .
Brion and Kumar give a detailed discussion of Frobenius splittings.
A fundamental property of Frobenius-split projective schemes is that the higher cohomology () of ample line bundles vanishes.
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