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arXiv · 1305.1684

Parity sheaves on the affine Grassmannian and the Mirkovi\'c-Vilonen conjecture

Pramod N. Achar·Laura Rider
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Abstract

We prove the Mirkovi\'c-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.

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BibTeXRIS

Pramod N. Achar, Laura Rider. 2013-05-08. Parity sheaves on the affine Grassmannian and the Mirkovi\'c-Vilonen conjecture. https://arxiv.org/abs/1305.1684

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