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The affine Grassmannian and the Springer resolution in positive characteristic

Part of: Lie groups (Co)homology theory

Published online by Cambridge University Press:  28 November 2016

Pramod N. Achar  and
Laura Rider
Pramod N. Achar
Affiliation:
Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA email pramod@math.lsu.edu
Laura Rider
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA email laurajoy@mit.edu
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Abstract

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An important result of Arkhipov–Bezrukavnikov–Ginzburg relates constructible sheaves on the affine Grassmannian to coherent sheaves on the dual Springer resolution. In this paper, we prove a positive-characteristic analogue of this statement, using the framework of ‘mixed modular sheaves’ recently developed by the first author and Riche. As an application, we deduce a relationship between parity sheaves on the affine Grassmannian and Bezrukavnikov’s ‘exotic t-structure’ on the Springer resolution.

Keywords

affine GrassmannianSpringer resolutionLanglands duality

MSC classification

Primary: 22E57: Geometric Langlands program
Secondary: 14F05: Sheaves, derived categories of sheaves and related constructions
Type
Research Article
Information
Compositio Mathematica , Volume 152 , Issue 12 , December 2016 , pp. 2627 - 2677
Copyright
© The Authors 2016 

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