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}, volume = {39}, year = {1989}, pages = {1-15}, doi = {10.5802/aif.1155}, mrnumber = {90i:14023}, zbl = {0658.14015}, language = {en}, url = {http://dml.mathdoc.fr/item/AIF_1989__39_1_1_0} }
Steen, Guido Van. The Schottky-Jung theorem for Mumford curves. Annales de l'Institut Fourier, Tome 39 (1989) pp. 1-15. doi : 10.5802/aif.1155. http://gdmltest.u-ga.fr/item/AIF_1989__39_1_1_0/
[1] Riemann surfaces, Graduate Texts in Mathematics, 71, Berlin, Heidelberg, New York, Springer-Verlag, 1980. | MR 82c:30067 | Zbl 0475.30001
, ,[2] Periods and Gauss-Manin Connection for Families of p-adic Schottky Groups, Math. Ann., 275 (1986), 425-453. | MR 87k:14028 | Zbl 0622.14018
,[3] On Non-Archimedean Representations of Abelian Varieties, Math. Ann., 196, (1972) 323-346. | MR 46 #7247 | Zbl 0255.14013
,[4] Schottky Groups and Mumford Curves, Lecture Notes in Math., 817, Berlin, Heidelberg, New York, Springer-Verlag, 1980. | MR 82j:10053 | Zbl 0442.14009
, ,[5] Nichtarchimedische Teichmüllerräume, Habitationsschrift, Bochum, Rühr Universität Bochum, 1975.
,[6] Prym varieties I. Contribution to Analysis, New York, Academic Press, 1974. | MR 52 #415 | Zbl 0299.14018
,[7] Familien von Schottky-Gruppen, Thesis, Bochum, Rühr Universität, 1986.
,[8] Etale Coverings of a Mumford Curve, Ann. Inst. Fourier, 33-1 (1983) 29-52. | Numdam | MR 84m:14026 | Zbl 0495.14017
,[9] Non-Archimedean Schottky Groups and Hyperelliptic Curves, Indag. Math., 45-1 (1983), 97-109. | MR 84h:14030 | Zbl 0513.14013
,[10] Note on Coverings of the Projective Line by Mumford Curves, Bull. Belg. Wisk. Gen., Vol. 38, Fasc. 1, Series B, (1984), 31-38. | MR 87m:14024 | Zbl 0622.14017
,[11] Prym Varieties for Mumford Curves, Proc. of the Conference on p-adic Analysis, Hengelhoef 1986, 197-207, Vrije Universiteit Brussel, 1987. | MR 89a:14036 | Zbl 0633.14015
,