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Derived Satake category and Affine Hecke category in mixed characteristics (2310.16244v2)
Published 24 Oct 2023 in math.NT, math.AG, and math.RT
Abstract: We construct a new affine Grassmannian which connects an equal characteristic affine Grassmannian and Zhu's Witt vector affine Grassmannian. As a result, we deduce the mixed characteristic version of the Bezrukavnikov-Finkelberg's derived Satake equivalence. By the same argument, we also obtain the mixed characteristic version of the Bezrukavnikov's equivalence between two categorifications of an affine Hecke algebra.