Seminar on Arithmetic Geometry

João Lourenço (University of Münster)

Abstract: Let k/F_p be an algebraically closed field and let G be any connected reductive group over a Laurent series field. To a given parahoric group model of G, we can consider its affine Grassmannian which carry interesting parahoric orbit closures, called Schubert varieties. It is known that these are always normal, Cohen-Macaulay, rational, etc. for almost all G, provided p is not torsion for G_der. The general strategy of proof goes back to Faltings, but it is far from ideal, as it relies on at least two constructions that cannot be done uniformly for all G. In this talk, I’ll explain a new proof that circumvents this via two techniques: inversion of adjunction for splinters following Bhatt et al. (joint with Cass); and a Serre presentation for distributions of loop groups.

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