Rigid local systems with monodromy group the Conway group Co_2

Abstract

We first develop some basic facts about hypergeometric sheaves on the multiplicative group ${\mathbb{G}}_m$ in characteristic $p>0$. Certain of their Kummer pullbacks extend to irreducible local systems on the affine line in characteristic $p>0$. One of these, of rank $23$ in characteristic $p=3$, turns out to have the Conway group ${\mathrm{Co}}_2$, in its irreducible orthogonal representation of degree $23$, as its arithmetic and geometric monodromy groups.