Rigid G2-Representations and motives of Type G2

TL;DR

This paper establishes a Hilbert Irreducibility result for motives with G2 as their motivic Galois group, advancing understanding of their residual realizations.

Contribution

It provides an effective Hilbert Irreducibility theorem specifically for motives with G2 motivic Galois group, a novel result in the field.

Findings

Proves an effective Hilbert Irreducibility result for G2-motives

Analyzes residual realizations of motives with G2 symmetry

Advances the theory of motives with exceptional Galois groups

Abstract

We prove an effective Hilbert Irreducibility result for residual realizations of a family of motives with motivic Galois group G2.