In general, Frobenius splitting only defines on field of characteristic $p$ (algebraically closed) field.

I am reading Brion and Kumar's book and I can see that there are geometric results can be proven by it on flag variety such as all higher cohomology groups of ample line bundle vanish, rational singularity, normality etc.

I am pretty curious about what kind of results over characteristic zero were/could be proven by Frobenius splitting technique. Can anyone give me some examples or reference about this aspect?