Newton Polygons of L-functions Associated to Deligne Polynomials

A conjecture of Le says that the Deligne polytope $Delta_d$ is generically ordinary if $pequiv 1 (!!bmod D(Delta_d))$, where $D(Delta_d)$ is a combinatorial constant determined by $Delta_d$. In this paper a counterexample is given to show that the conjecture is not true in general.