Masaharu Kaneda: Other aspects of Frobenius splitting

The Frobenius morphism on a reductive group does not split. On its algebra of distributions, however, the induced Frobenius morphism splits, which can also be quantized. On the flag variety G/P the comorphism of the Frobenius splits, the famous Frobenius splitting. We regard the comorphism as the sheafification of the imbedding of the socle of the corresponding G_1P-Verma module to the whole. We show that the quotient of the G_1P-Verma module to its head also splits upon sheafification. This is partly joint work with Michel Gros.