Parity sheaves on the affine Grassmannian and the Mirković–Vilonen conjecture
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Author(s)
Achar, Pramod N.
Rider, Laura
Date Issued
February 2016
Journal
Acta Mathematica
Publisher
Springer Netherlands
Citation
Achar, Pramod N., and Laura Rider. “Parity Sheaves on the Affine Grassmannian and the Mirković–Vilonen Conjecture.” Acta Math 215, no. 2 (December 2015): 183–216.
Version
Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s11511-016-0132-6
