The Schottky-Jung theorem for Mumford curves

Guido Van Steen

Annales de l'institut Fourier (1989)

  • Volume: 39, Issue: 1, page 1-15
  • ISSN: 0373-0956

Abstract

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The Schottky-Jung proportionality theorem, from which the Schottky relation for theta functions follows, is proved for Mumford curves, i.e. curves defined over a non-archimedean valued field which are parameterized by a Schottky group.

How to cite

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Steen, Guido Van. "The Schottky-Jung theorem for Mumford curves." Annales de l'institut Fourier 39.1 (1989): 1-15. <http://eudml.org/doc/74825>.

@article{Steen1989,
abstract = {The Schottky-Jung proportionality theorem, from which the Schottky relation for theta functions follows, is proved for Mumford curves, i.e. curves defined over a non-archimedean valued field which are parameterized by a Schottky group.},
author = {Steen, Guido Van},
journal = {Annales de l'institut Fourier},
keywords = {Schottky-Jung proportionality theorem; theta functions; Mumford curves},
language = {eng},
number = {1},
pages = {1-15},
publisher = {Association des Annales de l'Institut Fourier},
title = {The Schottky-Jung theorem for Mumford curves},
url = {http://eudml.org/doc/74825},
volume = {39},
year = {1989},
}

TY - JOUR
AU - Steen, Guido Van
TI - The Schottky-Jung theorem for Mumford curves
JO - Annales de l'institut Fourier
PY - 1989
PB - Association des Annales de l'Institut Fourier
VL - 39
IS - 1
SP - 1
EP - 15
AB - The Schottky-Jung proportionality theorem, from which the Schottky relation for theta functions follows, is proved for Mumford curves, i.e. curves defined over a non-archimedean valued field which are parameterized by a Schottky group.
LA - eng
KW - Schottky-Jung proportionality theorem; theta functions; Mumford curves
UR - http://eudml.org/doc/74825
ER -

References

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  1. [1] H.M. FARKAS, I. KRA, Riemann surfaces, Graduate Texts in Mathematics, 71, Berlin, Heidelberg, New York, Springer-Verlag, 1980. Zbl0475.30001MR82c:30067
  2. [2] L. GERRITZEN, Periods and Gauss-Manin Connection for Families of p-adic Schottky Groups, Math. Ann., 275 (1986), 425-453. Zbl0622.14018MR87k:14028
  3. [3] L. GERRITZEN, On Non-Archimedean Representations of Abelian Varieties, Math. Ann., 196, (1972) 323-346. Zbl0255.14013MR46 #7247
  4. [4] L. GERRITZEN, M. VAN DER PUT, Schottky Groups and Mumford Curves, Lecture Notes in Math., 817, Berlin, Heidelberg, New York, Springer-Verlag, 1980. Zbl0442.14009MR82j:10053
  5. [5] F. HERRLICH, Nichtarchimedische Teichmüllerräume, Habitationsschrift, Bochum, Rühr Universität Bochum, 1975. 
  6. [6] D. MUMFORD, Prym varieties I. Contribution to Analysis, New York, Academic Press, 1974. Zbl0299.14018MR52 #415
  7. [7] M. PIWEK, Familien von Schottky-Gruppen, Thesis, Bochum, Rühr Universität, 1986. 
  8. [8] M. VAN DER PUT, Etale Coverings of a Mumford Curve, Ann. Inst. Fourier, 33-1 (1983) 29-52. Zbl0495.14017MR84m:14026
  9. [9] G. VAN STEEN, Non-Archimedean Schottky Groups and Hyperelliptic Curves, Indag. Math., 45-1 (1983), 97-109. Zbl0513.14013MR84h:14030
  10. [10] G. VAN STEEN, Note on Coverings of the Projective Line by Mumford Curves, Bull. Belg. Wisk. Gen., Vol. 38, Fasc. 1, Series B, (1984), 31-38. Zbl0622.14017MR87m:14024
  11. [11] G. VAN STEEN, Prym Varieties for Mumford Curves, Proc. of the Conference on p-adic Analysis, Hengelhoef 1986, 197-207, Vrije Universiteit Brussel, 1987. Zbl0633.14015MR89a:14036

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