Number Theory Seminar

Schubert varieties are known to be Frobenius split in positive characteristic by the work of Mehta and Ramanathan. More recently, Bhatt showed that the full flag variety for GL_n is a splinter by entirely different methods. In this talk, we explain these concepts and show how to generalize Bhatt's result to all Schubert varieties for all reductive groups. Our methods apply equally well to affine Schubert varieties, which are of interest in the Langlands program and whose singularities are related to those of Shimura varieties. This is joint work with João Lourenço.