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.
Funding Statement
P. A. was supported by NSF Grant No. DMS-1001594. L. R. was supported by an NSF postdoctoral research fellowship.
Citation
Pramod N. Achar. Laura Rider. "Parity sheaves on the affine Grassmannian and the Mirković–Vilonen conjecture." Acta Math. 215 (2) 183 - 216, 2015. https://doi.org/10.1007/s11511-016-0132-6
Information