Specialization of polynomial covers of prime degree

Leonardo Zapponi

Vol. 214 (2004), No. 1, 161–183

DOI: 10.2140/pjm.2004.214.161

Abstract

Let K be a complete discrete valued field of unequal characteristic (0,p). The aim of this paper is to describe the semi-stable models for covers P_K¹ → P_K¹ of degree p, unramified outside r ≤ p points and totally ramified above one of them, under the assumtion that the ramification locus has a particular reduction type (which always occurs if r ≤ 4). We are principally concerned with the minimal semi-stable models which separate the ramified fibers.

Milestones

Received: 17 November 2002

Revised: 1 May 2003

Published: 1 March 2004