  In this article we study the modular properties of a family of cyclic
coverings of P^1 of degree N, in all odd characteristics. We compute the moduli
space of the corresponding algebraic stack over Z[1/2], as well as the Picard
groups over algebraically closed fields. We put special emphasis on the study
of the fibre of the stack at a prime of wild ramification; in particular we
show that the moduli space has good reduction at such a prime.
