Arbres de Hurwitz et automorphismes d'ordre p des disques et des couronnes p-adiques formels

Abstract

Let R be a complete discrete valuation ring of mixed characteristics (0,p). Given an order p-automorphism of a formal disc (or annulus) over R, we describe the minimal semi-stable model for which the specialisations of fixed points are distincts and lie in the smooth locus of the special fiber. The description leads to a combinatorial object called Hurwitz tree. Our main result is a necessary and sufficient condition for a Hurwitz tree to arise from an order p-automorphism.