arXiv:2405.03599math.AG
Proof of the geometric Langlands conjecture I: construction of the functor
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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.
I assume the reason this article has been published this week in particular is that a proof of the geometric Langlands conjecture has just been announced. [1] The first paper in the series was posted to the arXiv yesterday. [2] It’s obviously far too soon to say whether the…
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