Potential automorphy of $\widehat{G}$-local systems

TL;DR

This paper discusses advancing the Langlands program by establishing a potential automorphy result for $\\widehat{G}$-local systems, building on Vincent Lafforgue's recent groundbreaking work in positive characteristic.

Contribution

It extends Lafforgue's work by proving a potential automorphy theorem for $\\widehat{G}$-local systems, moving from Galois representations to automorphic forms.

Findings

Establishes potential automorphy for $\\widehat{G}$-local systems.

Builds on Lafforgue's automorphic--to--Galois correspondence.

Provides new tools for the Galois--to--automorphic direction.

Abstract

Vincent Lafforgue has recently made a spectacular breakthrough in the setting of the global Langlands correspondence for global fields of positive characteristic, by constructing the `automorphic--to--Galois' direction of the correspondence for an arbitrary reductive group $G$. We discuss a result that starts with Lafforgue's work and proceeds in the opposite (`Galois--to--automorphic') direction.