  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.
