2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60340Let 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.34 pages, to appear in Compositio MathematicaAlgebraic Geometrytext