- Acta Math.
- Volume 215, Number 2 (2015), 183-216.
Parity sheaves on the affine Grassmannian and the Mirković–Vilonen conjecture
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.
Acta Math., Volume 215, Number 2 (2015), 183-216.
Received: 4 July 2014
First available in Project Euclid: 30 January 2017
Permanent link to this document
Digital Object Identifier
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. https://projecteuclid.org/euclid.acta/1485802453