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

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

2000-11-15

arxiv.org/abs/math/0011098v1

Mathematics

Algebraic Geometry

34 pages, to appear in Compositio Mathematica

Scientific paper

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.

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