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

By Y. Henrio. 2000

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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.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e8b3c145f883546807bf4cb7115c3121cb039f36