Compatible systems of Galois representations associated to the exceptional group E6

TL;DR

This paper constructs compatible systems of l-adic Galois representations over CM fields with algebraic monodromy groups equal to the exceptional group E6, linking Galois representations to algebraic geometry and exceptional groups.

Contribution

It provides the first construction of compatible systems with monodromy group E6 over CM fields, expanding the understanding of Galois representations related to exceptional groups.

Findings

Constructed compatible systems over CM fields with E6 monodromy

Representations appear in the cohomology of algebraic varieties

Applicable to all primes l in the system

Abstract

We construct, over any CM field, compatible systems of l-adic Galois representations that appear in the cohomology of algebraic varieties and have (for all l) algebraic monodromy groups equal to the exceptional group of type E6.