English

Automorphic functions as the trace of Frobenius

Algebraic Geometry 2022-06-06 v2

Abstract

We prove that the trace of the Frobenius endofunctor of the category of automorphic sheaves with nilpotent singular support maps isomorphically to the space of unramified automorphic functions, settling a conjecture from [AGKRRV1]. More generally, we show that traces of Frobenius-Hecke functors produce shtuka cohomologies.

Keywords

Cite

@article{arxiv.2102.07906,
  title  = {Automorphic functions as the trace of Frobenius},
  author = {D. Arinkin and D. Gaitsgory and D. Kazhdan and S. Raskin and N. Rozenblyum and Y. Varshavsky},
  journal= {arXiv preprint arXiv:2102.07906},
  year   = {2022}
}