Rigid local systems with monodromy group the Conway group Co_3

TL;DR

This paper constructs specific rank 23 rigid local systems over characteristic 3 fields with monodromy groups isomorphic to the Conway group Co_3, linking algebraic geometry and finite group theory.

Contribution

It develops foundational aspects of rigid local systems and explicitly exhibits new examples with Co_3 monodromy groups in characteristic 3.

Findings

Existence of rank 23 rigid local systems with Co_3 monodromy

Explicit construction in characteristic 3

Connection between local systems and sporadic simple groups

Abstract

We first develop some basic facts about certain sorts of rigid local systems on the affine line in characteristic $p>0$. We then apply them to exhibit a number of rigid local systems of rank $23$ on the affine line in characteristic $p=3$ whose arithmetic and geometric monodromy groups are the Conway group $\mathrm{Co}_3$ in its orthogonal irreducible representation of degree $23$.