A Rigid Local System with Monodromy Group 2.J_2

TL;DR

This paper constructs a specific rank six rigid local system over an affine line in characteristic 5, with monodromy groups corresponding to the finite group 2.J_2, linking algebraic geometry and finite group theory.

Contribution

It explicitly exhibits a rigid local system with monodromy group 2.J_2, a novel connection between local systems and a sporadic finite simple group.

Findings

Monodromy group is 2.J_2 in a degree six representation.

Constructs a rigid local system in characteristic 5.

Links algebraic geometry with sporadic finite groups.

Abstract

We exhibit a rigid local system of rank six on the affine line in characteristic $p=5$ whose arithmetic and geometric monodromy groups are the finite group $2.J_2$ ($J_2$ the Hall-Janko sporadic group) in one of its two (Galois-conjugate) irreducible representation of degree six.