From geometric to function-theoretic Langlands (or how to invent shtukas)

Abstract

This is an informal note that explains that the classical Langlands theory over function fields can be obtained from the geometric one by taking the trace of Frobenius. The operation of taking the trace of Frobenius takes place at the categorical level, and this we deduce that the space of automorphic functions is the trace of the Frobenius on the category of automorphic sheaves.

References in corpus (1)

• One-loop corrections to holographic Wilson loop in AdS4xCP3

Cited by in corpus (5)

• Coherent sheaves on the stack of Langlands parameters
• Coherent Springer theory and the categorical Deligne-Langlands correspondence
• A toy model for the Drinfeld-Lafforgue shtuka construction
• Geometric Satake, categorical traces, and arithmetic of Shimura varieties
• Automorphic functions as the trace of Frobenius