Vers un algorithme pour la r\'eduction stable des rev\^etements p-cycliques de la droite projective sur un corps p-adique

Abstract

In his Ph. D. thesis, C. Lehr offers an algorithm which gives the stable model for p-cyclic covers of the projective line over a p-adic field under the conditions that the branch locus whose cardinal is m+1 has the so called equidistant geometry and m<p. In this note we give an algorithm also in the equidistant geometry case but without condition on m. In particular we are able to study the reduction at 2 of hyperelliptic curves with equidistant branch locus.