Specialization of polynomial covers of prime degree

Abstract

Let K be a complete field of unequal characteristics $(0,p)$. The aim of this paper is to describe the the semi-stable models for covers ${\mathbf{P}}_K^1@>>>{\mathbf{P}}_K^1$ of degree p, unramified outside $r\le p$ points and totally ramified above one of them, under the assumption that the ramified locus has a particular reduction type (which always occurs if $r\le 4$). We are principally concerned with the minimal semi-stable models which separate the ramified fibers.

20 pages, 19 figures