Computing finite Galois groups arising from automorphic forms

TL;DR

This paper constructs specific field extensions with Galois group G_2(F_p) by leveraging reductions of p-adic automorphic representations, advancing the understanding of Galois groups related to automorphic forms.

Contribution

It introduces a method to explicitly realize Galois groups G_2(F_p) from automorphic representations, linking automorphic forms to Galois theory.

Findings

Explicit construction of Galois extensions with group G_2(F_p)

Connection established between automorphic representations and Galois groups

Advancement in understanding automorphic forms' role in Galois theory

Abstract

We construct extensions of the field of rational numbers with the Galois group G_2(F_p) by reducing p-adic representations attached to automorphic representations.