Geometric Langlands in positive characteristic from characteristic zero

Dennis Gaitsgory; Sam Raskin

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arXiv · 2508.02237

Geometric Langlands in positive characteristic from characteristic zero

Dennis Gaitsgory·Sam Raskin

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Abstract

We establish part of the statement of the geometric Langlands conjecture for l-adic sheaves over a field of positive characteristic. Namely, we show that the category of automorphic sheaves with nilpotent singular support is equivalent to the appropriately defined category of ind-coherent sheaves on the union of some of the connected components of the stack of Langlands parameters.

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Dennis Gaitsgory, Sam Raskin. 2025-08-04. Geometric Langlands in positive characteristic from characteristic zero. https://arxiv.org/abs/2508.02237

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