## Acta Mathematica

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

#### 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.

#### Note

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

#### Article information

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

Dates
First available in Project Euclid: 30 January 2017

https://projecteuclid.org/euclid.acta/1485802453

Digital Object Identifier
doi:10.1007/s11511-016-0132-6

Mathematical Reviews number (MathSciNet)
MR3455233

Zentralblatt MATH identifier
1344.14016

Rights

#### Citation

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. https://projecteuclid.org/euclid.acta/1485802453

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