Artin characters, Hurwitz trees and the lifting problem

2008/10/20 by Louis Hugo Brewis, Stefan Wewers, Brewis, Louis Hugo +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology #math.AG #math.NT #msc:11G20 #msc:14D15 #msc:14H37

paper · pdf · doi:10.48550/arxiv.0810.3603

Remark 4.4 and Lemma 4.5 added

arxiv created 2008/12/02 · arxiv updated 2009/12/01

Abstract

We study finite groups of automorphisms of the p-adic open disk. In particular, we generalize results of Green, Matignon and Henrio from cyclic groups of order p to arbitrary finite groups. As an application, we produce a counterexample to a question of Chinburg, Guralnick and Harbater, concerning the local lifting problem for generalized quaternion groups.

Related

• An obstruction to the local lifting problem
• The local lifting problem for actions of finite groups on curves
• The Hurwitz tree obstruction for the refined local lifting problem
• Liftable self-similar groups and scale groups
• Hausdorff dimension in a family of self-similar groups