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

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.

27 pages. v4: added details to Section 2 and an appendix on sheaf functors on non-locally compact spaces

References in corpus (2)

• Modular representations of reductive groups and geometry of affine Grassmannians
• Constructible sheaves on affine Grassmannians and geometry of the dual nilpotent cone

Cited by in corpus (3)

• Exotic tilting sheaves, parity sheaves on affine Grassmannians, and the Mirkovic-Vilonen conjecture
• Modular perverse sheaves on flag varieties I: tilting and parity sheaves
• Notes on exotic and perverse-coherent sheaves