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2015 Parity sheaves on the affine Grassmannian and the Mirković–Vilonen conjecture
Pramod N. Achar, Laura Rider
Author Affiliations +
Acta Math. 215(2): 183-216 (2015). DOI: 10.1007/s11511-016-0132-6


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.


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Pramod N. Achar. Laura Rider. "Parity sheaves on the affine Grassmannian and the Mirković–Vilonen conjecture." Acta Math. 215 (2) 183 - 216, 2015.


Received: 4 July 2014; Published: 2015
First available in Project Euclid: 30 January 2017

zbMATH: 1344.14016
MathSciNet: MR3455233
Digital Object Identifier: 10.1007/s11511-016-0132-6

Primary: 22E57
Secondary: 14F05

Rights: 2016 © Institut Mittag-Leffler

Vol.215 • No. 2 • 2015
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