Acta Mathematica

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

Pramod N. Achar and Laura Rider

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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.


P. A. was supported by NSF Grant No. DMS-1001594. L. R. was supported by an NSF postdoctoral research fellowship.

Article information

Acta Math., Volume 215, Number 2 (2015), 183-216.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 22E57: Geometric Langlands program: representation-theoretic aspects [See also 14D24]
Secondary: 14F05: Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]

2016 © Institut Mittag-Leffler


Achar, Pramod N.; Rider, Laura. Parity sheaves on the affine Grassmannian and the Mirković–Vilonen conjecture. Acta Math. 215 (2015), no. 2, 183--216. doi:10.1007/s11511-016-0132-6.

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