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The affine Grassmannian and the Springer resolution in positive characteristic

Published online by Cambridge University Press:  28 November 2016

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.

Type
Research Article
Copyright
© The Authors 2016 

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