Geometry of an étale covering of the p-adic upper half plane
Annales de l'Institut Fourier, Volume 40 (1990) no. 1, p. 69-78

We describe the rigid geometry of the first layer in the tower of coverings of the p-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 p-adique construit par Drinfeld. En utilisant nos résultats, nous décrivons le fibré spécial stable en p 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},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {40},
     number = {1},
     year = {1990},
     pages = {69-78},
     doi = {10.5802/aif.1203},
     zbl = {0687.14019},
     mrnumber = {91i:11066},
     language = {en},
     url = {http://www.numdam.org/item/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, Volume 40 (1990) no. 1, pp. 69-78. doi : 10.5802/aif.1203. http://www.numdam.org/item/AIF_1990__40_1_69_0/

[1] V.G. Drinfeld, Elliptic modules, Math. USSR Sbornik, 23(4) (1976).

[2] V.G. Drinfeld, Coverings of p-adic symmetric regions, Functional Analysis and its Applications, 10(2) (1976), 29-40. | MR 54 #10281 | Zbl 0346.14010

[3] A. Kurihara, On some examples of equations defining Shimura curves and the Mumford uniformization, J. Fac. Sci. Univ. Tokyo, Sec. IA, 25 (1979). | MR 80e:14010 | Zbl 0428.14012

[4] D. Mumford, An analytic construction of degenerating curves over complete local rings, Compos. Math., 24 (1972), 129-174. | Numdam | MR 50 #4592 | Zbl 0228.14011

[5] M. Raynaud, Schémas en groupes de type (p,...,p), Bull. Soc. Math. France, 102 (1974). | Numdam | MR 54 #7488 | Zbl 0325.14020

[6] K. Ribet, Bimodules and abelian surfaces, Technical Report PAM-423, Center for Pure and Applied Mathematics, University of California, Berkeley, August 1988. | Zbl 0742.11033

[7] P. Schneider and U. Stuhler, The cohomology of p-adic symmetric spaces, preprint, 1988. | Zbl 0751.14016

[8] J. Teitelbaum, On Drinfeld's universal formal group over the p-adic upper half plane, Mathematische Annalen, 284 (1989), 647-674. | MR 90j:11050 | Zbl 0682.14032