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

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.

Survey article. Appeared in Proceedings of the ICM, 2018

References in corpus (2)

• On the automorphy of $l$-adic Galois representations with small residual image
• Independence of ell of Monodromy Groups