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

Dennis Gaitsgory; Sam Raskin

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arXiv · 2409.09856

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

Dennis Gaitsgory·Sam Raskin

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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.

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Dennis Gaitsgory, Sam Raskin. 2024-09-15. Proof of the geometric Langlands conjecture V: the multiplicity one theorem. https://arxiv.org/abs/2409.09856

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