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Unipotent nearby cycles and the cohomology of shtukas

Part of: Lie groups Curves

Published online by Cambridge University Press:  13 March 2023

Andrew Salmon
Andrew Salmon*
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA asalmon@mit.edu
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Abstract

We give cases in which nearby cycles commute with pushforward from sheaves on the moduli stack of shtukas to a product of curves over a finite field. The proof systematically uses the property that taking nearby cycles of Satake sheaves on the Beilinson–Drinfeld Grassmannian with parahoric reduction is a central functor together with a ‘Zorro's lemma’ argument similar to that of Xue [Smoothness of cohomology sheaves of stacks of shtukas, Preprint (2020), arXiv:2012.12833]. As an application, for automorphic forms at the parahoric level, we characterize the image of tame inertia under the Langlands correspondence in terms of two-sided cells.

Keywords

shtukasnearby cyclesparahoric subgroup

MSC classification

Primary: 14H60: Vector bundles on curves and their moduli
Secondary: 22E55: Representations of Lie and linear algebraic groups over global fields and adèle rings
Type
Research Article
Information
Compositio Mathematica , Volume 159 , Issue 3 , March 2023 , pp. 590 - 615
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Copyright
© 2023 The Author(s). The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence

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