no. 1
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.

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.

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.

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     title = {Geometry of an \'etale covering of the $p$-adic upper half plane},
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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. https://aif.centre-mersenne.org/articles/10.5802/aif.1203/

[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 | Zbl

[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 | Zbl

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

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

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

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

[8] J. Teitelbaum, 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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