Geometric Langlands in positive characteristic from characteristic zero

TL;DR

This paper advances the geometric Langlands program in positive characteristic by establishing an equivalence between automorphic sheaves with nilpotent singular support and ind-coherent sheaves on Langlands parameters, extending prior characteristic zero results.

Contribution

It proves a key part of the geometric Langlands conjecture in positive characteristic, linking automorphic sheaves to Langlands parameters in a new setting.

Findings

Category of automorphic sheaves with nilpotent singular support is equivalent to ind-coherent sheaves on Langlands parameters.

Establishes the conjectural correspondence in positive characteristic.

Extends geometric Langlands results from characteristic zero to positive characteristic.

Abstract

We establish part of the statement of the geometric Langlands conjecture for l-adic sheaves over a field of positive characteristic. Namely, we show that the category of automorphic sheaves with nilpotent singular support is equivalent to the appropriately defined category of ind-coherent sheaves on the union of some of the connected components of the stack of Langlands parameters.