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Unipotent nearby cycles and the cohomology of shtukas
Published online by Cambridge University Press: 13 March 2023
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.
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- Research Article
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- © 2023 The Author(s). The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence
References
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