Algebraic Geometry Seminar

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Lifting Galois Covers to Characteristic Zero with Non-Archimedean Analytic Geometry

Speaker: Daniele Turchetti, Institut de mathématiques de Jussieu

Location: Warren Weaver Hall 201

Date: Tuesday, February 25, 2014, 3:30 p.m.

Synopsis:

In this talk we deal with the so-called lifting problem on curves. Given an action of a finite group G over a smooth projective curve in characteristic p, does it always comes from reduction of an action of G in characteristic zero? It is known that the answer is yes when (|G|, p) = 1. When wild ramification phenomena appear, the question becomes much more complex. In order to study this problem, the notion of Hurwitz tree has been introduced and successfully exploited in the last ten years. This combinatorial object encodes both the geometry of fixed points and the ramification theory of the action. We show in this talk how these Hurwitz trees can be canonically embedded in the Berkovich unit disk. We will explain how this result sheds new light on the lifting problem and in which sense these embedded Hurwitz trees "parametrize" certain G-torsors.