In mathematics, a Frobenius splitting, introduced by Mehta and Ramanathan (1985), 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*.
Brion & Kumar (2005) 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.
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