Étale fundamental groups of non-archimedean analytic spaces

A. J. De Jong

Compositio Mathematica (1995)

  • Volume: 97, Issue: 1-2, page 89-118
  • ISSN: 0010-437X

How to cite


De Jong, A. J.. "Étale fundamental groups of non-archimedean analytic spaces." Compositio Mathematica 97.1-2 (1995): 89-118. <http://eudml.org/doc/90385>.

author = {De Jong, A. J.},
journal = {Compositio Mathematica},
keywords = {-crystals; -divisible groups; -adic period maps; rigid analytic space; Berkovich space; étale covering map; étale fundamental group},
language = {eng},
number = {1-2},
pages = {89-118},
publisher = {Kluwer Academic Publishers},
title = {Étale fundamental groups of non-archimedean analytic spaces},
url = {http://eudml.org/doc/90385},
volume = {97},
year = {1995},

AU - De Jong, A. J.
TI - Étale fundamental groups of non-archimedean analytic spaces
JO - Compositio Mathematica
PY - 1995
PB - Kluwer Academic Publishers
VL - 97
IS - 1-2
SP - 89
EP - 118
LA - eng
KW - -crystals; -divisible groups; -adic period maps; rigid analytic space; Berkovich space; étale covering map; étale fundamental group
UR - http://eudml.org/doc/90385
ER -


  1. [SGA1] Revêtements étales et groupe fondamentale, 1960-61. Dirigé par A. Grothendieck, Lecture notes in mathematics224, Springer-Verlag, Berlin-Heidelberg -New York, 1971. Zbl0234.14002MR354651
  2. [SGA4] Théorie des topos et cohomologie étale des schemas, 1963-64. 1960-61. Dirigé par M. Artin, A. Grothendieck and J.-L. Verdier, Lecture notes in mathematics, 269, 270, 305, Springer Verlag, Berlin-Heidelberg- New York, 1972-1973. Zbl0245.00002
  3. [B1] V.G. Berkovich, Spectral theory and analytic geometry over non-archimedean fields, Mathematical surveys and monographs, 33, American mathematical society, Providence1990. Zbl0715.14013MR1070709
  4. [B2] V.G. Berkovich, Étale cohomology for non-Archimedean analytic spaces, Publ. Math. I.H.E.S.78, 5-161 (1993). Zbl0804.32019MR1259429
  5. [B] P Berthelot, Cohomologie rigide et cohomologie rigide à support propre, Version provisoire du 9/08/91. 
  6. [Bou] N. Bourbaki, Topologie Génerale, chapitres 1 à 5, Masson, Paris-Milan- Barcelone-Mexico, 1990. 
  7. [BL] S. Bosch and W. Lütkebohmert, Formal and rigid geometry, Math. Ann.295 (1993), 291-317. Zbl0808.14017MR1202394
  8. [En] R Engelking, General topology, Warszawa, 1977. Zbl0373.54002MR500780
  9. [FM] J Fresnel and M. Matignon, Sur les espaces analytiques quasi-compacts de dimension 1 sur un corps valué complet ultramétrique, Annali di Matematica pura ed applicata (4) 145, 159-210 (1986). Zbl0623.32020MR886711
  10. [Gi] J. Giraud, Cohomologie non abelienne, Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen 179, Springer-Verlag, Berlin-Heidelberg- New York1971. Zbl0226.14011MR344253
  11. [HG] M.J. Hopkins and B.H. Gross, Equivariant vector bundles on the Lubin-Tate moduli space, Contemporary Mathematics158, 1994. Zbl0807.14037MR1263712
  12. [HG2] M.J. Hopkins and B.H. Gross, The rigid analyitc period mapping, Lubin-Tate space, and stable homotopy theory, Preprint. Zbl0857.55003MR1217353
  13. [Hu] R Huber, Étale cohomology of rigid analytic varieties and adic spaces, Preprint, July 1994. MR1734903
  14. [dJ] A.J. de Jong, Crystalline Dieudonné module theory via formal and rigid geometry, to appear. Zbl0864.14009
  15. [JP] A.J. de Jong and M. van der Put, Étale cohomology of rigid analytic spaces, Preprint of the University of Groningen. Zbl0922.14012
  16. [KM] N Katz and B. Mazur, Arithmetic moduli of elliptic curves, Annals of mathematics studies108, Princeton university press, Princeton, New Jersey1985. Zbl0576.14026MR772569
  17. [La] M Lazard, Groupes analytiques p-adiques, Publications mathematiques I.H.E.S., 26, 1965. Zbl0139.02302MR209286
  18. [LP] Q Liu and M. van der Put, On one dimesional separated rigid spaces. To appear in Indagationes Mathematicae. Zbl0922.14013
  19. [Ma] G.A. Margulis, Discrete subgroups of semisimple Lie groups, Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Folge-Bd.17. Springer-Verlag, Berlin-Heidelberg-New York1989. Zbl0732.22008MR1090825
  20. [RZ] M Rapoport and T. Zink, Period spaces for p-divisible groups, Preprint, Bergische Universität Wuppertal and Universität Bielefeld, November 1994. MR1393439
  21. [SS] P Schneider and U. Stuhler, The cohomology of p-adic symmetric spaces, Invent. math.105, 47-122 (1991). Zbl0751.14016MR1109620
  22. [Se1] J.-P. Serre, Abelian l-adic representations and elliptic curves, Addison-Wesley publishing company, inc. Reading, Massachusetts -New York1989. Zbl0709.14002MR1043865
  23. [Se2] J.-P. Serre, Lie algebras and Lie Groups, Lecture notes in mathematics1500, Springer Verlag, Berlin- Heidelberg-New York1992. Zbl0742.17008MR1176100
  24. [T] J Tate, p-divisible groups, local fields, Nuffic summer school at Driebergen, Springer-Verlag, Berlin-Heidelberg -New York1967. Zbl0157.27601MR231827
  25. [Y] J.-K. Yu, A-divisible modules, period maps, and quasi-canonical liftings, Thesis Harvard University. 

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