Formes non tempérées pour U 3 et conjectures de Bloch–Kato

Joël Bellaïche; Gaëtan Chenevier

Annales scientifiques de l'École Normale Supérieure (2004)

  • Volume: 37, Issue: 4, page 611-662
  • ISSN: 0012-9593

How to cite

top

Bellaïche, Joël, and Chenevier, Gaëtan. "Formes non tempérées pour $U\left(3\right)$ et conjectures de Bloch–Kato." Annales scientifiques de l'École Normale Supérieure 37.4 (2004): 611-662. <http://eudml.org/doc/82641>.

@article{Bellaïche2004,
author = {Bellaïche, Joël, Chenevier, Gaëtan},
journal = {Annales scientifiques de l'École Normale Supérieure},
language = {fre},
number = {4},
pages = {611-662},
publisher = {Elsevier},
title = {Formes non tempérées pour $U\left(3\right)$ et conjectures de Bloch–Kato},
url = {http://eudml.org/doc/82641},
volume = {37},
year = {2004},
}

TY - JOUR
AU - Bellaïche, Joël
AU - Chenevier, Gaëtan
TI - Formes non tempérées pour $U\left(3\right)$ et conjectures de Bloch–Kato
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2004
PB - Elsevier
VL - 37
IS - 4
SP - 611
EP - 662
LA - fre
UR - http://eudml.org/doc/82641
ER -

References

top
  1. [1] Arthur J., Clozel L., Simple Algebras, Base Change and the Advanced Theory of the Trace Formula, Ann. of Math. Stud., vol. 120, Princeton University Press, 1989. Zbl0682.10022MR1007299
  2. [2] Artin E., Tate J., Class Field Theory, Benjamin, 1968. Zbl0176.33504MR223335
  3. [3] Bellaïche J., Congruences endoscopiques et représentations galoisiennes, Thèse de l'université Paris 11, janvier 2002. 
  4. [4] Bellaïche J., À propos d'un lemme de Ribet, Rend. Sem. Univ. Padova109 (2003) 47-62. Zbl1048.20032MR1997986
  5. [5] Bellaïche J., Graftieaux P., Représentations sur un anneau de valuation discrète complet, Math. Ann., à paraître. Zbl1178.20040MR2207872
  6. [6] Bellaïche J., Graftieaux P., Augmentation du niveau pour U 3 , Preprint de l’université de Nice. MR2214894
  7. [7] Bernstein I.N., Zelevinsky A.V., Induced representations of reductive p-adic groups I, Ann. Sci. École Norm. Sup. (4)10 (1977) 441-472. Zbl0412.22015MR579172
  8. [8] Blasco L., Description du dual admissible de U 2 , 1 F par la théorie des types de C. Bushnell et P. Kutzko, Manuscripta Math.107 (2) (2002) 151-186. Zbl1108.22011MR1894738
  9. [9] Blasius D., Rogawski J., Tate class and arithmetic quotient of two-ball, in: Langlands R., Ramakhrisnan D. (Eds.), The Zeta Functions of Picard Modular Surfaces, Publications C.R.M., Montréal, 1992, pp. 421-443. Zbl0828.14012MR1155236
  10. [10] Blasius D., Rogawski J., Zeta functions of Shimura varieties, in: Motives, in: Proc. Sympos. Pure Math., vol. 55. Zbl0827.11033MR1265563
  11. [11] Blasius D., Rogawski J., Motives for Hilbert modular forms, Invent. Math.114 (1993) 55-87. Zbl0829.11028MR1235020
  12. [12] Borel A., Some finiteness properties of adele groups over number fields, IHÉS Publ. Math.16 (1963) 5-30. Zbl0135.08902MR202718
  13. [13] Borel A., Admissible representations of a semi-simple group over a local field with vectors fixed under an Iwahori subgroup, Invent. Math.35 (1976) 233-259. Zbl0334.22012MR444849
  14. [14] Borel A., Casselman W., Automorphic forms, representations, and L-functions, in: Proc. Sympos. Pure Math., vol. 33, 1977, Corvallis. Zbl0412.10017
  15. [15] Bosch S., Güntzer U., Remmert R., Non Archimedian Analysis, in: Grundlehren der mathematischen Wissenschaften, vol. 261, Springer-Verlag. Zbl0539.14017
  16. [16] Bushnell C., Smooth representations of p-adic group, ICM 1998, pp. 770–779. Zbl0856.22021MR1403977
  17. [17] Bushnell C., Kutzko P., Smooth representations of reductive p-adic groups: structure theory via types, Proc. London Math. Soc. (3)77 (1997) 582-634. Zbl0911.22014MR1643417
  18. [18] Bushnell C., Kutzko P., Semi-simple types, Compositio Math.119 (1999) 53-117. Zbl0933.22027
  19. [19] Buzzard K., Eigenvarieties, 2002, en préparation. 
  20. [20] Cartier P., Representations of p-adic groups: a survey, in: Proc. Sympos. Pure Math., vol. 33, 1977, pp. 111-155, Part I. Zbl0421.22010MR546593
  21. [21] Casselman W., The unramified principal series of p-adic groups. I. The spherical function, Compositio Math.40 (3) (1980) 387-406. Zbl0472.22004MR571057
  22. [22] Chenevier G., Familles p-adiques de formes automorphes pour G L n , J. Reine Angew. Math.570 (2004) 143-217. Zbl1093.11036MR2075765
  23. [23] Chenevier G., Familles p-adiques de formes automorphes et applications aux conjectures de Bloch–Kato, Thèse de l'université Paris 7, 2003. 
  24. [24] Choucroun F., Analyse harmonique des groupes d'automorphismes d'arbres de Bruhat–Tits, Mém. Soc. Math. France (N.S.) (58) (1994) 170. Zbl0840.43019MR1294542
  25. [25] Clozel L., Représentations galoisiennes associées aux représentations automorphes autoduales de G L n , IHÉS Publ. Math.73 (1991) 97-145. Zbl0739.11020MR1114211
  26. [26] Clozel L., Labesse J.-P., Changement de base pour les représentations cohomologiques de certains groupes unitaires, in: Astérisque, vol. 257, SMF, 1998, Appendice A. 
  27. [27] Coleman R., P-adic Banach spaces & families of modular forms, Invent. Math.127 (1997) 417-479. Zbl0918.11026MR1431135
  28. [28] Curtis C., Reiner I., Representation Theory of Finite Groups and Associative Algebras, Wiley, 1962. Zbl0131.25601MR1013113
  29. [29] Faltings G., Cristalline cohomology and p-adic Galois representations, in: Algebraic Analysis and Number Theory, JAMI Conference, 1988, pp. 25-90. Zbl0805.14008MR1463696
  30. [30] Fontaine J.-M., Le corps des périodes p-adiques, in: Périodes p-adiques, Astérisque, vol. 223, Société mathématique de France, 1994, pp. 59-111, exposé 2. Zbl0940.14012MR1293971
  31. [31] Fontaine J.-M., Représentations p-adiques semi-stables, in: Périodes p-adiques, Astérisque, vol. 223, Société mathématique de France, 1994, pp. 113-184, exposé 3. Zbl0865.14009MR1293972
  32. [32] Fontaine J.-M., Perrin-Riou B., Autour des conjectures de Bloch–Kato: cohomologie galoisienne et valeurs de fonctions L, in: Motives, Proc. Sympos. Pure Math., vol. 55, 1994, pp. 599-706, part 1. Zbl0821.14013MR1265546
  33. [33] Gordon B.B., Canonical models of Picard modular surfaces, in: Langlands R., Ramakhrisnan D. (Eds.), The Zeta Functions of Picard Modular Surfaces, Publications C.R.M., Montréal, 1992, pp. 1-27. Zbl0756.14011MR1155224
  34. [34] Harris M., On the local Langlands correspondence, in: Proceedings ICM 2002, vol. 2, 2002, pp. 583-597. Zbl1151.11351MR1957067
  35. [35] Harris M., Taylor R., The Geometry and Cohomology of Some Simple Shimura Varieties, Ann. Math. Stud., vol. 151, 2001. Zbl1036.11027MR1876802
  36. [36] Humphreys J.E., Reflection Groups and Coxeter Groups, Cambridge Studies in Advanced Mathematics, vol. 29. Zbl0768.20016
  37. [37] Katz N., Messing W., Some consequences of the Riemann Hypothesis for varieties over finite fields, Invent. Math.23 (1974) 73-77. Zbl0275.14011MR332791
  38. [38] Keys D., Principal series representations of special unitary groups over local fields, Compositio Math.51 (1) (1984) 115-130. Zbl0547.22009MR734788
  39. [39] Kisin M., Overconvergent modular forms and the Fontaine–Mazur conjecture, Invent. Math.153 (2003) 363-454. Zbl1045.11029MR1992017
  40. [40] Kottwitz R., Points on some Shimura varieties over finite fields, J. Amer. Math. Soc.5 (2) (1992). Zbl0796.14014MR1124982
  41. [41] Labesse J.-P., Cohomologie, stabilisation et changement de base, Astérisque, vol. 257, SMF, 1998. Zbl1024.11034MR1695940
  42. [42] Langlands R., Ramakhrisnan D. (Eds.), The Zeta Functions of Picard Modular Surfaces, Publications C.R.M., Montréal, 1992. Zbl0752.00024MR1155223
  43. [43] Matsumura H., Commutative ring theory, Cambridge Studies in Adv. Math., vol. 8, 1980. Zbl0603.13001
  44. [44] Mazur B., The theme of p-adic variation, in: Arnold V., Atiyah M., Lax P., Mazur B. (Eds.), Math.: Frontiers and Perspectives, AMS, 2000. Zbl0959.14008MR1754790
  45. [45] Motives, Proc. Sympos. Pure Math., vol. 55. 
  46. [46] Périodes p-adiques, Astérisque, vol. 223, Société mathématique de France, 1994. Zbl0802.00019MR1293969
  47. [47] Perrin-Riou B., Représentations p-adiques ordinaires, in: Périodes p-adiques, Astérisque, vol. 223, Société mathématique de France, 1994, pp. 209-220, exposé 4. Zbl1043.11532MR1293973
  48. [48] Ribet K., A modular construction of unramified extensions of Q ζ p , Invent. Math.34 (3) (1976) 151-162. Zbl0338.12003MR419403
  49. [49] Rogawski J., Analytic expression for the number of points mod p, in: Langlands R., Ramakhrisnan D. (Eds.), The Zeta Functions of Picard Modular Surfaces, Publications C.R.M., Montréal, 1992, pp. 65-109. Zbl0821.14015MR1155227
  50. [50] Rogawski J., The multiplicity formula for A-packets, in: Langlands R., Ramakhrisnan D. (Eds.), The Zeta Functions of Picard Modular Surfaces, Publications C.R.M., Montréal, 1992, pp. 395-419. Zbl0823.11027MR1155235
  51. [51] Rogawski J., On modules over the Hecke algebra of a p-adic group, Invent. Math.79 (1985) 443-465. Zbl0579.20037MR782228
  52. [52] Rogawski J., Automorphic Representations of Unitary Groups in Three Variables, Ann. of Math. Stud., vol. 123, Princeton University Press, 1990. Zbl0724.11031MR1081540
  53. [53] Rouquier R., Caractérisations des caractères et pseudo-caractères, J. Algebra180 (1996) 571-586. Zbl0857.16013MR1378546
  54. [54] Rubin K., The “main conjectures” of Iwasawa theory for imaginary quadratic fields, Invent. Math.103 (1) (1991) 25-68. Zbl0737.11030
  55. [55] Rubin K., Euler systems, Ann. of Math. Stud.147 (2000). Zbl0977.11001MR1749177
  56. [56] Serre J.-P., Endomorphismes complètement continus des espaces de Banach p-adiques, IHÉS Publ. Math.12 (1962) 69-85. Zbl0104.33601MR144186
  57. [57] Sen S., Continuous cohomology and p-adic Galois representations, Invent. Math.62 (1980) 89-116. Zbl0463.12005MR595584
  58. [58] Sen S., An infinite dimensional Hodge–Tate theory, Bull. Soc. Math. France121 (1993) 13-34. Zbl0786.11067MR1207243
  59. [59] Grothendieck A., Artin M., Verdier J.-L., Théorie des topos et cohomologie étale des schémas, Séminaire de géométrie algébrique IV, exposé XVI. Zbl0234.00007
  60. [60] Skinner C., Urban E., Sur les déformations p-adiques des formes de Saito–Kurokawa, C. R. Acad. Sci. Paris Sér. I335 (2002) 581-586. Zbl1024.11030MR1941298
  61. [61] Tate J., Number theoretic background, in: Automorphic Forms, Representations and L-Functions, Part 2, Proc. Sympos. Pure Math., vol. 33, 1977, pp. 3-26. Zbl0422.12007MR546607
  62. [62] Taylor R., Galois representations attached to Siegel modular forms of low weight, Duke Math. J.63 (1991) 281-332. Zbl0810.11033MR1115109
  63. [63] Tits J., Reductive groups over local fields, Part I, in: Proc. Sympos. Pure Math., vol. 33, 1977, pp. 29-69. Zbl0415.20035MR546588
  64. [64] Zelevinsky A.V., Induced representations of reductive p-adic groups II. On irreducible representations of G L n , Ann. Sci. École Norm. Sup. (4)13 (1980) 165-210. Zbl0441.22014MR584084

NotesEmbed ?

top

You must be logged in to post comments.