Acta Mathematica

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

Pramod N. Achar and Laura Rider

Full-text: Open access

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

Permanent link to this document
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

Subjects
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]

Rights
2016 © Institut Mittag-Leffler

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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References

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