We describe the rigid geometry of the first layer in the tower of coverings of the -adic upper half plane constructed by Drinfeld. Using our results, we describe the stable fiber at p of certain Shimura curves.
Nous décrivons la géométrie analytique rigide de la première couche dans la tour de revêtements du demi-plan -adique construit par Drinfeld. En utilisant nos résultats, nous décrivons le fibré spécial stable en de certaines courbes de Shimura.
@article{AIF_1990__40_1_69_0,
author = {Teitelbaum, Jeremy},
title = {Geometry of an \'etale covering of the $p$-adic upper half plane},
journal = {Annales de l'Institut Fourier},
pages = {69--78},
year = {1990},
publisher = {Institut Fourier},
address = {Grenoble},
volume = {40},
number = {1},
doi = {10.5802/aif.1203},
mrnumber = {91i:11066},
zbl = {0687.14019},
language = {en},
url = {https://www.numdam.org/articles/10.5802/aif.1203/}
}
TY - JOUR AU - Teitelbaum, Jeremy TI - Geometry of an étale covering of the $p$-adic upper half plane JO - Annales de l'Institut Fourier PY - 1990 SP - 69 EP - 78 VL - 40 IS - 1 PB - Institut Fourier PP - Grenoble UR - https://www.numdam.org/articles/10.5802/aif.1203/ DO - 10.5802/aif.1203 LA - en ID - AIF_1990__40_1_69_0 ER -
%0 Journal Article %A Teitelbaum, Jeremy %T Geometry of an étale covering of the $p$-adic upper half plane %J Annales de l'Institut Fourier %D 1990 %P 69-78 %V 40 %N 1 %I Institut Fourier %C Grenoble %U https://www.numdam.org/articles/10.5802/aif.1203/ %R 10.5802/aif.1203 %G en %F AIF_1990__40_1_69_0
Teitelbaum, Jeremy. Geometry of an étale covering of the $p$-adic upper half plane. Annales de l'Institut Fourier, Tome 40 (1990) no. 1, pp. 69-78. doi: 10.5802/aif.1203
[1] , Elliptic modules, Math. USSR Sbornik, 23(4) (1976).
[2] , Coverings of p-adic symmetric regions, Functional Analysis and its Applications, 10(2) (1976), 29-40. | Zbl | MR
[3] , On some examples of equations defining Shimura curves and the Mumford uniformization, J. Fac. Sci. Univ. Tokyo, Sec. IA, 25 (1979). | Zbl | MR
[4] , An analytic construction of degenerating curves over complete local rings, Compos. Math., 24 (1972), 129-174. | Zbl | MR | Numdam
[5] , Schémas en groupes de type (p,...,p), Bull. Soc. Math. France, 102 (1974). | Zbl | MR | Numdam
[6] , Bimodules and abelian surfaces, Technical Report PAM-423, Center for Pure and Applied Mathematics, University of California, Berkeley, August 1988. | Zbl
[7] and , The cohomology of p-adic symmetric spaces, preprint, 1988. | Zbl
[8] , On Drinfeld's universal formal group over the p-adic upper half plane, Mathematische Annalen, 284 (1989), 647-674. | Zbl | MR
Cité par Sources :
