Proof of the geometric Langlands conjecture V: the multiplicity one theorem

Gaitsgory, Dennis; Raskin, Sam

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Proof of the geometric Langlands conjecture V: the multiplicity one theorem

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Gaitsgory, Dennis
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.48550/arXiv.2409.09856
(Preprint)

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2409.09856v1.pdf
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Citation

Gaitsgory, D., & Raskin, S. (submitted). Proof of the geometric Langlands conjecture V: the multiplicity one theorem.

Cite as: https://hdl.handle.net/21.11116/0000-000F-E6AA-E

Abstract

This is the final paper in the series of five, in which we prove the geometric Langlands conjecture (GLC). We conclude the proof of GLC by showing that there exists a unique (up to tensoring up by a vector space) Hecke eigensheaf corresponding to an irreducible local system (hence, the title of the paper). We achieve this by analyzing the geometry of the stack of local systems.