학술논문
Parity sheaves on the affine Grassmannian and the Mirković-Vilonen conjecture.
Document Type
Article
Author
Source
Subject
*GRASSMANN manifolds
*DIFFERENTIAL topology
*MANIFOLDS (Mathematics)
*LOGICAL prediction
*SCHUBERT varieties
*FERMAT'S little theorem
*TWIN prime conjecture
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Language
ISSN
0001-5962
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. [ABSTRACT FROM AUTHOR]