Uniformisation p -adique des variétés de Shimura

Jean-François Boutot

Séminaire Bourbaki (1996-1997)

  • Volume: 39, page 307-322
  • ISSN: 0303-1179

How to cite


Boutot, Jean-François. "Uniformisation $p$-adique des variétés de Shimura." Séminaire Bourbaki 39 (1996-1997): 307-322. <http://eudml.org/doc/110233>.

author = {Boutot, Jean-François},
journal = {Séminaire Bourbaki},
keywords = {-adic uniformization; Shimura variety; moduli space; -divisible group; formal group; Langlands conjectures; Shimura curves; Bruhat-Tits building; uniformizing formal scheme},
language = {fre},
pages = {307-322},
publisher = {Société Mathématique de France},
title = {Uniformisation $p$-adique des variétés de Shimura},
url = {http://eudml.org/doc/110233},
volume = {39},
year = {1996-1997},

AU - Boutot, Jean-François
TI - Uniformisation $p$-adique des variétés de Shimura
JO - Séminaire Bourbaki
PY - 1996-1997
PB - Société Mathématique de France
VL - 39
SP - 307
EP - 322
LA - fre
KW - -adic uniformization; Shimura variety; moduli space; -divisible group; formal group; Langlands conjectures; Shimura curves; Bruhat-Tits building; uniformizing formal scheme
UR - http://eudml.org/doc/110233
ER -


  1. [B] V.G. Berkovich - Etale cohomology for non-archimedean analytic spaces, Publ. Math. I.H.E.S.78 (1993), 5-161. Zbl0804.32019MR1259429
  2. [Be] P. Berthelot - Cohomologie rigide et cohomologie à supports propres, prépublication 96-03, Inst. Rech. Math. Rennes, 1996. 
  3. [BC] J.-F. Boutot, H. Carayol - Uniformisation p-adique des courbes de Shimura: les théorèmes de Cherednik et de Drinfeld, Astérisque196-197 (1991), 45-158. Zbl0781.14010MR1141456
  4. [BZ] J.-F. Boutot, Th. Zink - The p-adic uniformisation of Shimura curves, preprint 95-107, Sonderforschungsbereich343, Universität Bielefeld, 1995. 
  5. [C] H. Carayol - Non-abelian Lubin-Tate theory, Automorphic forms, Shimura varieties and L-functions, vol. II, Perspectives in Math.11, Academic Press (1990), 15-39. Zbl0704.11049MR1044827
  6. [Ch] I.V. Cherednik - Uniformization of algebraic curves by discrete subgroups of PGL2(kw) with compact quotients, Math. USSR Sbornik29 (1976), 55-78. Zbl0379.14010
  7. [De] P. Deligne - Travaux de Shimura, Séminaire Bourbaki, vol. 1970/71, Exp. 389, Lecture Notes in Math.244, Springer Verlag (1971), 123-165. Zbl0225.14007MR498581
  8. [Dr1] V.G. Drinfeld - Elliptic Modules, Math. USSR Sbornik23 (1974), 561-592. Zbl0321.14014MR384707
  9. [Dr2] V.G. Drinfeld - Coverings of p-adic symmetric regions, Funct. Anal. and Appl.10 (1976), 107-115. Zbl0346.14010MR422290
  10. [F] G. Faltings - The trace formula and Drinfeld's upper halfplane, Duke Math. J.76 (1994), 467-482. Zbl0855.11061MR1302321
  11. [F] J.-M. Fontaine - Modules galoisiens, modules filtres et anneaux de Barsotti-Tate, Astérisque65 (1979), 3-80. Zbl0429.14016MR563472
  12. [Ge] A. Genestier - Espaces symétriques de Drinfeld, Astérisque234 (1996). Zbl0912.14015MR1393015
  13. [GH1] B. Gross, M. Hopkins - The rigid analytic period mapping, Lubin-Tate space, and stable homotopy theory, Bull. Amer. Math. Soc.30 (1994), 76-86. Zbl0857.55003MR1217353
  14. [GH2] B. Gross, M. Hopkins - Equivariant vector bundles on the Lubin-Tate moduli space, Contemp. Math.158 (1994), 23-88. Zbl0807.14037MR1263712
  15. [G] A. Grothendieck - Groupes de Barsotti-Tate et cristaux, Actes du Congr. Internat. Math., Nice1970, vol.1, Gauthier-Villars (1971), 431-436. Zbl0244.14016MR578496
  16. [H] M. Harris - Supercuspidal representations in the cohomology of Drinfeld upper half-spaces; elaboration of Carayol's program, Inventiones Math.129 (1997), 75-119. Zbl0886.11029MR1464867
  17. [Ko1] R.E. Kottwitz - Isocrystals with additional structure, Compositio Math.56 (1985), 201-220. Zbl0597.20038MR809866
  18. [Ko2] R.E. Kottwitz - Shimura varieties and λ-adic representations, Automorphic forms, Shimura varieties and L-functions, vol. I , Perspectives in Math.10, Academic Press (1990), 161-209. Zbl0743.14019
  19. [Ko3] R.E. Kottwitz - Points on some Shimura varieties over finite fields, Journal Amer. Math. Soc.5 (1992), 373-444. Zbl0796.14014MR1124982
  20. [L] G. Lafaille - Constructions de groupes p-divisibles: le cas de dimension 1 , Astérisque65 (1979), 103-124. Zbl0438.14028MR563474
  21. [LT] J. Lubin, J. Tate - Formal moduli for one parameter formal Lie groups, Bull. Soc. Math. France94 (1966), 49-60. Zbl0156.04105MR238854
  22. [Me] W. Messing - The crystals associated to Barsotti-Tate groups : with applications to abelian schemes, Lecture Notes in Math.264, Springer Verlag (1972). Zbl0243.14013MR347836
  23. [M] D. Mumford - An analytic construction of degenerating curves over complete local rings, Compositio Math.24 (1972), 239-272. Zbl0241.14020MR352106
  24. [Mu] G.A. Mustafin - Non archimedean uniformization, Math. USSR Sbornik34 (1978), 187-214. Zbl0411.14006MR476763
  25. [R1] M. Rapoport - On the bad reduction of Shimura varieties, Automorphic forms, Shimura varieties and L-functions, vol. II, Perspectives in Math.11, Academic Press (1990), 15-39. Zbl0716.14010MR1044832
  26. [R2] M. Rapoport - Non-archimedean period domains, Proc. Internat. Congress Math., Zürich1994, vol. 1, Birkhäuser Verlag (1995), 423-434. Zbl0874.11046MR1403942
  27. [RR] M. Rapoport, M. Richartz - On the classification and specialization of Fisocrystals with additional structure, Compositio Math.103 (1996), 153-181. Zbl0874.14008MR1411570
  28. [RZ] M. Rapoport, Th. Zink - Period spaces for p-divisible groups, Annals of Math. Studies141, Princeton University Press (1996). Zbl0873.14039MR1393439
  29. [Ra1] M. Raynaud - Géométrie analytique rigide d'après Tate, Kiehl,... , Bull. Soc. Math. France, Mém.39-40 (1974), 319-327. Zbl0299.14003MR470254
  30. [Ra2] M. Raynaud - Construction analytique de courbes en géométrie non archimedienne (d'après David Mumford), Séminaire Bourbaki, vol. 1972/73, Exp. 427, Lecture Notes in Math.383, Springer Verlag (1974), 171-185. Zbl0294.14017MR469923
  31. [SS] P. Schneider, U. Stuhler - The cohomology of p-adic symmetric spaces, Inventiones Math.105 (1991), 47-122. Zbl0751.14016MR1109620
  32. [T] J. Tate - Rigid analytic spaces, Inventiones Math.12 (1971), 257-289. Zbl0212.25601MR306196
  33. [To] B. Totaro - Tensor products in p-adic Hodge theory, Duke Math. Journal83 (1996), 79-104. Zbl0873.14019MR1388844
  34. [VV] M. Van Der Put , H. Voskuil - Symmetric spaces associated to split algebraic groups over a local field, J. reine angew. Math.433 (1992), 69-100. Zbl0753.14018MR1191600
  35. [Va] Y. Varshavsky - P-adic uniformization of unitary Shimura varieties, preprint Jerusalem (1995). MR1659274
  36. [Y] J.-K. Yu - On the moduli of quasi-canonical liftings, Compositio Math.96 (1995), 296-321. Zbl0866.14029MR1327148

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