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Drinfeld's lemma for F-isocrystals, II: Tannakian approach
Published online by Cambridge University Press: 01 December 2023
Abstract
We prove a Tannakian form of Drinfeld's lemma for isocrystals on a variety over a finite field, equipped with actions of partial Frobenius operators. This provides an intermediate step towards transferring V. Lafforgue's work on the Langlands correspondence over function fields from $\ell$-adic to $p$-adic coefficients. We also discuss a motivic variant and a local variant of Drinfeld's lemma.
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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
Footnotes
The first author is supported by NSF grants DMS-1802161 and DMS-2053473 and the UC San Diego Warschawski Professorship. The second author is supported by the National Natural Science Foundation of China grants 12222118 and 12288201 and the CAS Project for Young Scientists in Basic Research grant YSBR-033. D.X. is grateful to Xinwen Zhu for suggesting this question and helpful discussions.
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