Abstract
We prove the Mirković–Vilonen conjecture: the integral local intersection cohomology groups of spherical Schubert varieties on the affine Grassmannian have no p-torsion, as long as p is outside a certain small and explicitly given set of prime numbers. (Juteau has exhibited counterexamples when p is a bad prime.) The main idea is to convert this topological question into an algebraic question about perverse-coherent sheaves on the dual nilpotent cone using the Juteau–Mautner–Williamson theory of parity sheaves.
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P. A. was supported by NSF Grant No. DMS-1001594. L. R. was supported by an NSF postdoctoral research fellowship.
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Achar, P.N., Rider, L. Parity sheaves on the affine Grassmannian and the Mirković–Vilonen conjecture. Acta Math 215, 183–216 (2015). https://doi.org/10.1007/s11511-016-0132-6
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DOI: https://doi.org/10.1007/s11511-016-0132-6