Etale coverings of a Mumford curve

Marius Van Der Put

Annales de l'institut Fourier (1983)

  • Volume: 33, Issue: 1, page 29-52
  • ISSN: 0373-0956

Abstract

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Let the field K be complete w.r.t. a non-archimedean valuation. Let X / K be a Mumford curve, i.e. the irreducible components of the stable reduction of X have genus 0. The abelian etale coverings of X are constructed using the analytic uniformization Ω → X and the theta-functions on X . For a local field K one rediscovers G . Frey’s description of the maximal abelian unramified extension of the field of rational functions of X .

How to cite

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Put, Marius Van Der. "Etale coverings of a Mumford curve." Annales de l'institut Fourier 33.1 (1983): 29-52. <http://eudml.org/doc/74574>.

@article{Put1983,
abstract = {Let the field $K$ be complete w.r.t. a non-archimedean valuation. Let $X/K$ be a Mumford curve, i.e. the irreducible components of the stable reduction of $X$ have genus 0. The abelian etale coverings of $X$ are constructed using the analytic uniformization $\Omega \rightarrow X$ and the theta-functions on $X$. For a local field $K$ one rediscovers $G$. Frey’s description of the maximal abelian unramified extension of the field of rational functions of $X$.},
author = {Put, Marius Van Der},
journal = {Annales de l'institut Fourier},
keywords = {complete non-archimedean valued field; Mumford curve; abelian etale coverings; theta-functions; field of rational functions},
language = {eng},
number = {1},
pages = {29-52},
publisher = {Association des Annales de l'Institut Fourier},
title = {Etale coverings of a Mumford curve},
url = {http://eudml.org/doc/74574},
volume = {33},
year = {1983},
}

TY - JOUR
AU - Put, Marius Van Der
TI - Etale coverings of a Mumford curve
JO - Annales de l'institut Fourier
PY - 1983
PB - Association des Annales de l'Institut Fourier
VL - 33
IS - 1
SP - 29
EP - 52
AB - Let the field $K$ be complete w.r.t. a non-archimedean valuation. Let $X/K$ be a Mumford curve, i.e. the irreducible components of the stable reduction of $X$ have genus 0. The abelian etale coverings of $X$ are constructed using the analytic uniformization $\Omega \rightarrow X$ and the theta-functions on $X$. For a local field $K$ one rediscovers $G$. Frey’s description of the maximal abelian unramified extension of the field of rational functions of $X$.
LA - eng
KW - complete non-archimedean valued field; Mumford curve; abelian etale coverings; theta-functions; field of rational functions
UR - http://eudml.org/doc/74574
ER -

References

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  1. [1] J. FRESNEL, M. van der PUT, Géométrie analytique rigide et applications, Progress in Math., Birkhäuser Verlag, 1981. Zbl0479.14015MR83g:32001
  2. [2] G. FREY, Maximal abelsche Erweiterung von Funktionenkörper über lokalen Köpern, Archiv der Mathematik, Vol. 28 (1977), 157-168. Zbl0352.14012MR56 #12009
  3. [3] L. GERRITZEN, M. van der PUT, Schottky groups and Mumford curves, Lect. Notes in Math., 817 (1980). Zbl0442.14009MR82j:10053
  4. [4] M. van der PUT, Stable reductions of algebraic curves, University of Groningen preprint, ZW-8019 (1982). 
  5. [5] M. van der PUT, Les fonctions theta d'une courbe de Mumford, Sém. d'Analyse Ultramétrique, déc. 1981, I.H.P. 
  6. [6] G. van STEEN, Hyperelliptic Curves defined by Schottky groups over a non-archimedean valued field, Thesis Antwerpen U.I.A., 1981. 

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