Title

Parity sheaves on the affine Grassmannian and the Mirković–Vilonen conjecture

Document Type

Article

Publication Date

12-1-2015

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.

Publication Source (Journal or Book title)

Acta Mathematica

First Page

183

Last Page

216

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