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Proof of the geometric Langlands conjecture I: construction of the functor

MPS-Authors
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Gaitsgory,  Dennis
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.48550/arXiv.2405.03599
(Preprint)

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2405.03599.pdf
(Preprint), 509KB

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Citation

Gaitsgory, D., & Raskin, S. (submitted). Proof of the geometric Langlands conjecture I: construction of the functor.


Cite as: https://hdl.handle.net/21.11116/0000-000F-E685-7
Abstract
We construct the geometric Langlands functor in one direction (from the automorphic to the spectral side) in characteristic zero settings (i.e., de Rham and Betti). We prove that various forms of the conjecture (de Rham vs Betti, restricted vs. non-restricted, tempered vs. non-tempered) are equivalent. We also discuss structural properties of Hecke eigensheaves.