Nombre de points des variétés de Shimura sur un corps fini

Laurent Clozel

Séminaire Bourbaki (1992-1993)

  • Volume: 35, page 121-149
  • ISSN: 0303-1179

How to cite

top

Clozel, Laurent. "Nombre de points des variétés de Shimura sur un corps fini." Séminaire Bourbaki 35 (1992-1993): 121-149. <http://eudml.org/doc/110167>.

@article{Clozel1992-1993,
author = {Clozel, Laurent},
journal = {Séminaire Bourbaki},
keywords = {Langlands conjecture; zeta functions of Shimura varieties; number of points of Shimura varieties over a finite field},
language = {fre},
pages = {121-149},
publisher = {Société Mathématique de France},
title = {Nombre de points des variétés de Shimura sur un corps fini},
url = {http://eudml.org/doc/110167},
volume = {35},
year = {1992-1993},
}

TY - JOUR
AU - Clozel, Laurent
TI - Nombre de points des variétés de Shimura sur un corps fini
JO - Séminaire Bourbaki
PY - 1992-1993
PB - Société Mathématique de France
VL - 35
SP - 121
EP - 149
LA - fre
KW - Langlands conjecture; zeta functions of Shimura varieties; number of points of Shimura varieties over a finite field
UR - http://eudml.org/doc/110167
ER -

References

top
  1. [C] Automorphic Forms, Representations, and L-functions, Proceedings of the Corvallis Conference, A. Borel et W. Casselman eds, Proc. Symp. Pure Math.33, AMS, Providence, 1979, I, II. 
  2. [AA] Automorphic Forms, Shimura Varieties, and L-functions, Proceedings of the Ann Arbor Conference, L. Clozel et J.S. Milne eds, Academic Press., 1990, I, II. Zbl0684.00004
  3. [1] D. Blasius et J. Rogawski. — Zeta functions of Shimura varieties, à paraître dans le volume de la conférence de Seattle (1991) sur les "Motifs". Zbl0827.11033
  4. [2] A. Borel. — Automorphic L-functions, in [C], II, 27-62. 
  5. [3] L. Breen, J.-P. Labesse eds. — Variétés de Shimura et fonctions L, Publ. Math. Univ.ParisVII, 6, s.d. Zbl0517.00003
  6. [4] J.-L. Brylinski et J.-P. Labesse. — Cohomologie d'intersection et fonctions L de certaines variétés de Shimura, Ann. Sci. E.N.S. (IV) 17 (1984), 361-412. Zbl0553.12005MR777375
  7. [5] H. Carayol. — Sur les représentations l-adiques associées aux formes modulaires de Hilbert, Ann. Sci. E.N.S.19 (1986), 409-468. Zbl0616.10025MR870690
  8. [6] H. Carayol. — Variétés de Drinfel'd compactes, d'après Laumon, Rapoport et Stuhler, Sém. Bourbaki, 1991-92, Exposé 756. Zbl0801.14005
  9. [7] L. Clozel. — Nombres de Tamagawa des groupes semi-simples (d'après Kottwitz), Sém. Bourbaki, 1988-89, Exposé 702. Zbl0705.11028
  10. [8] P. Deligne. — Travaux de Shimura, Sém. Bourbaki, fev. 1971, Exposé 389. Zbl0225.14007MR498581
  11. [9] P. Deligne. — Variétés de Shimura, in [C], II, 247-290. 
  12. [10] P. Deligne. — Motifs et groupe de Taniyama, in Deligne, Milne, Ogus, Shih, "Hodge Cycles, Motives, and Shimura Varieties", Springer L.N. Math.900, 261-279. Zbl0499.14001
  13. [11] M. Eichler. — Quaternäre quadratische Formen and die Riemannsche Vermutung für die Kongruenzzetafunktion, Arch. Math.5 (1954), 355- 366. Zbl0059.03804MR63406
  14. [12] T. Honda. — Isogeny classes of abelian varieties over finite fields, J. Math. Soc. Japan20 (1968), 83-95. Zbl0203.53302MR229642
  15. [13] N. Katz et B. Mazur. — Arithmetic moduli of elliptic curves, Annals of Math. Studies, Princeton Univ. Press., Princeton, 1985. Zbl0576.14026MR772569
  16. [14] R. Kottwitz. — Shimura varieties and twisted orbital integrals, Math. Ann.269, (1984), 287-300. Zbl0533.14009MR761308
  17. [15] R. Kottwitz. — Isocrystals with additonal structure, Compositio Math.56, (1985), 201-220. Zbl0597.20038MR809866
  18. [16] R. Kottwitz. — Shimura varieties and λ-adic representations, in [AA], I, 161-209. Zbl0743.14019
  19. [17] R. Kottwitz. - Points on Shimura varieties over finite fields, Journ. A.M.S.5, (1992), 373-444. Zbl0796.14014MR1124982
  20. [18] R. Kottwitz. — On the λ-adic representations associated to some simple Shimura varieties, Inv. Math., 108, (1992), 653-665. Zbl0765.22011
  21. [19] J.-P. Labesse. — La formule des traces d'Arthur-Selberg, Sém. Bourbaki, 1986, Exposé 636. Zbl0592.22011
  22. [20] R.P. Langlands. — Some contemporary problems with origins in the Jugendtraum, in "Mathematical Developments Arising from Hilbert Problems", Proc. Sympos. Pure Math.28, (1976), 401-418. Zbl0345.14006MR437500
  23. [21] R.P. Langlands. — Shimura varieties and the Selberg trace formula, Can. J. Math.29 (1977), 1292-1299. Zbl0385.14005MR498400
  24. [22] R.P. Langlands. — On the zeta-functions of some simple Shimura varieties, Can. J. Math.31, (1979), 1121-1216. Zbl0444.14016MR553157
  25. [23] R.P. Langlands. — Automorphic representations, Shimura varieties and motives, in [C], II, 205-246. Zbl0447.12009MR546619
  26. [24] R.P. Langlands. — Base change for GL(2), Annals of Math. Studies, Princeton Univ. Press., Princeton, 1980. Zbl0444.22007MR574808
  27. [25] R.P. Langlands, M. Rapoport. — Shimuravarietäten und Gerben, J. Reine Angew. Math.378, (1987), 113-220. Zbl0615.14014MR895287
  28. [26] R.P. Langlands, D. Ramakrishnan eds. — The zêta functions of Picard Modular Surfaces, Publ. du Centre de Recherches Mathématiques, Montréal, 1992. Zbl0752.00024MR1155223
  29. [27] J.S. Milne. — Points on Shimura varieties modp, in [C], II, 165-184. MR546616
  30. [28] J.S. Milne. — The conjecture of Langlands and Rapoport for Siegel modular varieties, Bull. Amer. Math. Soc.24, (1991), 335-341. Zbl0743.11031MR1071030
  31. [29] J.S. Milne. — The conjecture of Langlands and Rapoport for Siegel modular varieties, preprint, 1990. 
  32. [30] J.S. Milne. — Canonical Models of (Mixed) Shimura Varieties and Automorphic Vector Bundles, in [AA], I, 283-414. Zbl0704.14016MR1044823
  33. [31] M. Rapoport. — On the Bad Reduction of Shimura Varieties, in [AA], II, 253-321. Zbl0716.14010MR1044832
  34. [32] H. Reimann, T. Zink. — Der Dieudonnémodul einer polarisierten abelschen Mannigfaltigkeit vom CM-typ, Ann. of Math.128, (1988), 461-482. Zbl0674.14030MR970608
  35. [33] H. Reimann, T. Zink. — The good reduction of Shimura varieties associated to quaternion algebras over a totally real number field, preprint. 
  36. [34] G. Shimura. — Introduction to the arithmetic theory of automorphic functions, Iwanami Shoten and Princeton Univ. Press., 1971. Zbl0221.10029MR314766
  37. [35] Y. Taniyama. — Complex multiplication of abelian varieties and its applications to number theory, Publ. Math. Soc. Japan, 6, 1961. Zbl0112.03502MR125113
  38. [36] J. Tate. — Classes d'isogénie des variétés abéliennes sur un corps fini (d'après T. Honda), Sém. Bourbaki, 1968, Exposé 352. Zbl0212.25702
  39. [37] T. Zink. — Isogenieklassen von Punkten von Shimuramannigfaltigkeiten mit Werten in einem endlichen Körper, Math. Nachr.112, (1983), 103- 124. Zbl0604.14029MR726854

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.