Rigid local systems with monodromy group the Conway group Co₃

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 $23$.