Geometry of an étale covering of the -adic upper half plane

Jeremy Teitelbaum

Annales de l'institut Fourier (1990)

  • Volume: 40, Issue: 1, page 69-78
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Teitelbaum, Jeremy. "Geometry of an étale covering of the $p$-adic upper half plane." Annales de l'institut Fourier 40.1 (1990): 69-78. <http://eudml.org/doc/74874>.

@article{Teitelbaum1990,
abstract = {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.},
author = {Teitelbaum, Jeremy},
journal = {Annales de l'institut Fourier},
keywords = {p-adic uniformization; formal group; tower of coverings of the p-adic upper half plane; Shimura curves},
language = {eng},
number = {1},
pages = {69-78},
publisher = {Association des Annales de l'Institut Fourier},
title = {Geometry of an étale covering of the $p$-adic upper half plane},
url = {http://eudml.org/doc/74874},
volume = {40},
year = {1990},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 40
IS - 1
SP - 69
EP - 78
AB - 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.
LA - eng
KW - p-adic uniformization; formal group; tower of coverings of the p-adic upper half plane; Shimura curves
UR - http://eudml.org/doc/74874
ER -

References

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  1. [1] V.G. DRINFELD, Elliptic modules, Math. USSR Sbornik, 23(4) (1976). 
  2. [2] V.G. DRINFELD, Coverings of p-adic symmetric regions, Functional Analysis and its Applications, 10(2) (1976), 29-40. Zbl0346.14010MR54 #10281
  3. [3] A. KURIHARA, On some examples of equations defining Shimura curves and the Mumford uniformization, J. Fac. Sci. Univ. Tokyo, Sec. IA, 25 (1979). Zbl0428.14012MR80e:14010
  4. [4] D. MUMFORD, An analytic construction of degenerating curves over complete local rings, Compos. Math., 24 (1972), 129-174. Zbl0228.14011MR50 #4592
  5. [5] M. RAYNAUD, Schémas en groupes de type (p,...,p), Bull. Soc. Math. France, 102 (1974). Zbl0325.14020MR54 #7488
  6. [6] K. RIBET, Bimodules and abelian surfaces, Technical Report PAM-423, Center for Pure and Applied Mathematics, University of California, Berkeley, August 1988. Zbl0742.11033
  7. [7] P. SCHNEIDER and U. STUHLER, The cohomology of p-adic symmetric spaces, preprint, 1988. Zbl0751.14016
  8. [8] J. TEITELBAUM, On Drinfeld's universal formal group over the p-adic upper half plane, Mathematische Annalen, 284 (1989), 647-674. Zbl0682.14032MR90j:11050

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