no. 1
The Schottky-Jung theorem for Mumford curves
Annales de l'Institut Fourier, Tome 39 (1989) no. 1, pp. 1-15.

Le théorème de Schottky-Jung, qui a pour conséquence la relation de Schottky pour les fonctions theta, est prouvé pour des courbes de Mumford, c’est-à-dire, des courbes définies sur un corps non-archimédien qui sont paramétrisées par un groupe de Schottky.

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.

@article{AIF_1989__39_1_1_0,
     author = {Steen, Guido Van},
     title = {The {Schottky-Jung} theorem for {Mumford} curves},
     journal = {Annales de l'Institut Fourier},
     pages = {1--15},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {39},
     number = {1},
     year = {1989},
     doi = {10.5802/aif.1155},
     zbl = {0658.14015},
     mrnumber = {90i:14023},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1155/}
}
TY  - JOUR
AU  - Steen, Guido Van
TI  - The Schottky-Jung theorem for Mumford curves
JO  - Annales de l'Institut Fourier
PY  - 1989
SP  - 1
EP  - 15
VL  - 39
IS  - 1
PB  - Institut Fourier
PP  - Grenoble
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.1155/
DO  - 10.5802/aif.1155
LA  - en
ID  - AIF_1989__39_1_1_0
ER  - 
%0 Journal Article
%A Steen, Guido Van
%T The Schottky-Jung theorem for Mumford curves
%J Annales de l'Institut Fourier
%D 1989
%P 1-15
%V 39
%N 1
%I Institut Fourier
%C Grenoble
%U https://aif.centre-mersenne.org/articles/10.5802/aif.1155/
%R 10.5802/aif.1155
%G en
%F AIF_1989__39_1_1_0
Steen, Guido Van. The Schottky-Jung theorem for Mumford curves. Annales de l'Institut Fourier, Tome 39 (1989) no. 1, pp. 1-15. doi : 10.5802/aif.1155. https://aif.centre-mersenne.org/articles/10.5802/aif.1155/

[1] H.M. Farkas, I. Kra, Riemann surfaces, Graduate Texts in Mathematics, 71, Berlin, Heidelberg, New York, Springer-Verlag, 1980. | MR | Zbl

[2] L. Gerritzen, Periods and Gauss-Manin Connection for Families of p-adic Schottky Groups, Math. Ann., 275 (1986), 425-453. | EuDML | MR | Zbl

[3] L. Gerritzen, On Non-Archimedean Representations of Abelian Varieties, Math. Ann., 196, (1972) 323-346. | EuDML | MR | Zbl

[4] L. Gerritzen, M. Van Der Put, Schottky Groups and Mumford Curves, Lecture Notes in Math., 817, Berlin, Heidelberg, New York, Springer-Verlag, 1980. | MR | Zbl

[5] F. Herrlich, Nichtarchimedische Teichmüllerräume, Habitationsschrift, Bochum, Rühr Universität Bochum, 1975.

[6] D. Mumford, Prym varieties I. Contribution to Analysis, New York, Academic Press, 1974. | MR | Zbl

[7] M. Piwek, Familien von Schottky-Gruppen, Thesis, Bochum, Rühr Universität, 1986.

[8] M. Van Der Put, Etale Coverings of a Mumford Curve, Ann. Inst. Fourier, 33-1 (1983) 29-52. | EuDML | Numdam | MR | Zbl

[9] G. Van Steen, Non-Archimedean Schottky Groups and Hyperelliptic Curves, Indag. Math., 45-1 (1983), 97-109. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

Cité par Sources :