Wildly Ramified Actions and Surfaces of General Type Arising from Artin-Schreier Curves

We analyse the diagonal quotient for products of certain Artin--Schreier curves. The smooth models are almost always surfaces of general type, with Chern slopes tending asymptotically to 1. The calculation of numerical invariants relies on a close examination of the relevant quotient singularity in characteristic p. It turns out that the canonical model has q-1 rational double points of type A_{q-1}, and embeds as a divisor of degree q in P^3, which is in some sense reminiscent of the classical Kummer quartic.