Nearby cycles of parahoric shtukas, and a fundamental lemma for base change
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Author(s)
Feng, Tony L.
Date Issued
March 2020
Journal
Selecta Mathematica
Publisher
Springer Science and Business Media LLC
Citation
Feng, Tony. "Nearby cycles of parahoric shtukas, and a fundamental lemma for base change." Selecta Mathematica 26, 2 (March 2020): 21 © 2020 Springer Nature Switzerland AG
Version
Author's final manuscript
Abstract
Using the Langlands–Kottwitz paradigm, we compute the trace of Frobenius composed with Hecke operators on the cohomology of nearby cycles, at places of parahoric reduction, of perverse sheaves on certain moduli stacks of shtukas. Following an argument of Ngô, we then use this to give a geometric proof of a base change fundamental lemma for parahoric Hecke algebras for GL[subscript n] over local function fields. This generalizes a theorem of Ngô, who proved the base change fundamental lemma for spherical Hecke algebras for GL[subscript n] over local function fields, and extends to positive characteristic (for GL[subscript n]) a fundamental lemma originally introduced and proved by Haines for p-adic local fields.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00029-020-0546-z
