2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65227Let 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 $\bold P^1_K@>>>\bold P^1_K$ of degree p, unramified outside $r\leq p$ points and totally ramified above one of them, under the assumption that the ramified locus has a particular reduction type (which always occurs if $r\leq4$). We are principally concerned with the minimal semi-stable models which separate the ramified fibers.20 pages, 19 figuresAlgebraic GeometryNumber Theory14H30 14H45 14E20 11G20text