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}
}