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
Recommended Citation
Achar, P., & Rider, L. (2015). Parity sheaves on the affine Grassmannian and the Mirković–Vilonen conjecture. Acta Mathematica, 215 (2), 183-216. https://doi.org/10.1007/s11511-016-0132-6