October 20, 2025Open Access

Local and global Langlands conjecture(s) over function fields

Key Points

The conjectures aim to clarify the relationship between automorphic functions and spectral parameters.
The primary focus is on the langlands conjecture, attempting to bridge different mathematical realms.
These ideas build on the existing langlands program and address questions about function fields.
The exploration of automorphic functions is significant for understanding advanced mathematical structures.

Abstract

This is a write-up for the plenary ICM talk, 2026. The goal of this paper is to propose a set of conjectures whose aim is to answer the basic question of the Langlands program (over function fields): how to describe the space of automorphic functions in terms of the spectral side (i.e., Langlands parameters)?

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Cite This Study

Dennis Gaitsgory (Mon,) studied this question.

synapsesocial.com/papers/68f5fcce8d54a28a75cf1d8b https://doi.org/https://doi.org/10.48550/arxiv.2509.24902

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