Rigid local systems and potential automorphy: The $G_2$-case

TL;DR

This paper demonstrates the potential automorphy of specific Galois representations valued in the exceptional group G_2 using a rigid local system, advancing understanding in number theory and automorphic forms.

Contribution

It introduces a novel application of a rigid local system to establish potential automorphy for G_2-valued Galois representations, a new approach in the field.

Findings

Proves potential automorphy of G_2 Galois representations

Utilizes a specific rigid local system for the proof

Advances methods in automorphy lifting techniques

Abstract

We use a certain rigid local system in order to prove the potential automorphy of certain Galois representations with values in $G_2,$ found by N. Katz and the author.