  The Bogomolov-Miyaoka-Yau inequality asserts that the Chern numbers of a
surface X of general type in characteristic 0 satisfy the inequality c_1^2 <=
3c_2, a consequence of which is (K_X^2)/chi(O_X) <= 9. This inequality fails in
characteristic p, and here we produce infinite families of counterexamples for
large p. Our method parallels a construction of Hirzebruch, and relies on a
construction of abelian covers due to Catanese and Pardini.
