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Mumford curves and Mumford groups in positive characteristic

Voskuil, H. H. & van der Put, M., 1-Jan-2019, In : Journal of algebra. 517, p. 119-166 48 p.

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  • Mumford curves and Mumford groups in positive characteristic

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DOI

  • Harm H. Voskuil
  • Marius van der Put

A Mumford group is a discontinuous subgroup Gamma of PGL(2) (K), where K denotes a non archimedean valued field, such that the quotient by Gamma is a curve of genus 0. As abstract group Gamma is an amalgam of a finite tree of finite groups. For K of positive characteristic the large collection of amalgams having two or three branch points is classified. Using these data Mumford curves with a large group of automorphisms are discovered. A long combinatorial proof, involving the classification of the finite simple groups, is needed for establishing an upper bound for the order of the group of automorphisms of a Mumford curve. Orbifolds in the category of rigid spaces are introduced. For the projective line the relations with Mumford groups and singular stratified bundles are studied. This paper is a sequel to [26]. Part of it clarifies, corrects and extends work of G. Cornelissen, F. Kato and K. Kontogeorgis. (C) 2018 Elsevier Inc. All rights reserved.

Original languageEnglish
Pages (from-to)119-166
Number of pages48
JournalJournal of algebra
Volume517
Publication statusPublished - 1-Jan-2019

    Keywords

  • Rigid geometry, Discontinuous groups, Mumford curves, Mumford groups, Amalgams, Orbifolds, Stratified bundles, MAXIMAL AUTOMORPHISM GROUP, STRATIFIED BUNDLES, PGL(2)(K), SUBGROUPS

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