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Cohomology of line bundles on the flag variety $SL_3/B$ can be computed using the Bott-Borel-Weil formula in the case the ground field has characteristic zero. In this way one obtains an explicit formula for the dimensions of the cohomology groups.

Is there a similar formula in the positive characteristic case?

If there is even a generalization to general flag varieties $G/P$, I'd be interested in hearing about that too.

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