A rigid local system with monodromy group \(2.J_{2}\) (Q2422164)

The authors consider rigid local systems on the affine line in finite characteristic \(p\) and define their arithmetic and geometric monodromy groups \(G_{\mathrm{arith}}\) and \(G_{\mathrm{geom}}\). For \(p=5\), they exhibit such a rank six system with \(G_{\mathrm{arith}}=G_{\mathrm{geom}}=2.J_2\) (where \(J_2\) is the Hall-Janko sporadic group) in one of its two (Galois-conjugate) irreducible representation of degree six.