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.
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.
@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},
publisher = {Institut Fourier},
address = {Grenoble},
volume = {40},
number = {1},
year = {1990},
doi = {10.5802/aif.1203},
mrnumber = {91i:11066},
zbl = {0687.14019},
language = {en},
url = {http://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 - http://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 http://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. http://www.numdam.org/articles/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. | MR | Zbl
[3] , On some examples of equations defining Shimura curves and the Mumford uniformization, J. Fac. Sci. Univ. Tokyo, Sec. IA, 25 (1979). | MR | Zbl
[4] , An analytic construction of degenerating curves over complete local rings, Compos. Math., 24 (1972), 129-174. | Numdam | MR | Zbl
[5] , Schémas en groupes de type (p,...,p), Bull. Soc. Math. France, 102 (1974). | Numdam | MR | Zbl
[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. | MR | Zbl
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