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

2016/06/30 by Dennis Gaitsgory, Gaitsgory, Dennis · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1606.09608

openalex publication_date 2016/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Cited by

• Geometric Satake, categorical traces, and arithmetic of Shimura varieties

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