English

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

Algebraic Geometry 2016-07-01 v1

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.

Keywords

Cite

@article{arxiv.1606.09608,
  title  = {From geometric to function-theoretic Langlands (or how to invent shtukas)},
  author = {Dennis Gaitsgory},
  journal= {arXiv preprint arXiv:1606.09608},
  year   = {2016}
}
R2 v1 2026-06-22T14:39:56.403Z