Formes de Maass et représentations galoisiennes

Guy Henniart

Séminaire Bourbaki (1988-1989)

  • Volume: 31, page 277-302
  • ISSN: 0303-1179

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Henniart, Guy. "Formes de Maass et représentations galoisiennes." Séminaire Bourbaki 31 (1988-1989): 277-302. <http://eudml.org/doc/110111>.

@article{Henniart1988-1989,
author = {Henniart, Guy},
journal = {Séminaire Bourbaki},
keywords = {Langlands-Weil conjecture; cuspidal automorphic representation; algebraicity; eigenvalues of Hecke operators},
language = {fre},
pages = {277-302},
publisher = {Société Mathématique de France},
title = {Formes de Maass et représentations galoisiennes},
url = {http://eudml.org/doc/110111},
volume = {31},
year = {1988-1989},
}

TY - JOUR
AU - Henniart, Guy
TI - Formes de Maass et représentations galoisiennes
JO - Séminaire Bourbaki
PY - 1988-1989
PB - Société Mathématique de France
VL - 31
SP - 277
EP - 302
LA - fre
KW - Langlands-Weil conjecture; cuspidal automorphic representation; algebraicity; eigenvalues of Hecke operators
UR - http://eudml.org/doc/110111
ER -

References

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  1. [Ar 1] J. Arthur - On some problems suggested by the trace formula in Lie groups and representations II, Springer L.N.M. vol. 1041, 1983, 1-49. Zbl0541.22011MR748504
  2. [Ar 2] J. Arthur - On a family of distributions obtained from orbits, Can. J. Math.38, 1986, 179-214. Zbl0593.22015MR835041
  3. [AC] J. Arthur, L. Clozel - Simple algebras, base change, and the advanced theory of the trace formula, Annals of Math. Studies, Princeton University Press, 1989. Zbl0682.10022MR1007299
  4. [AMRT] A. Ash, D. Mumford, M. Rapoport, Y.-S. Tai - Smooth compactifcation of locally symmetric varieties, Brooklin, Mass. Math. Sci. Press, 1975. Zbl0334.14007MR457437
  5. [Bl] D. Blasius - Automorphic forms and Galois representations : some examples, à paraître dans Proc. of a conference on Shimura varieties, Ann Arbor, 1988. Zbl0718.11018
  6. [BCR 1] D. Blasius, L. Clozel, D. Ramakrishnan - Algébricité de l'action des opérateurs de Hecke sur certaines formules de Maass, C.R.A.S. Paris305, 1987, 705-708. Zbl0628.10035MR920047
  7. [BCR 2] D. Blasius, L. Clozel, D. Ramakrishnan - Opérateurs de Hecke et formules de Maass : application de la formule des traces, C.R.A.S. Paris306, 1988, 59-62. Zbl0639.10020MR929109
  8. [BHR] D. Blasius, M. Harris, D. Ramakrishnan - Coherent cohomology, limits of discrete series and Maass forms of Galois type, notes préliminaires. 
  9. [B-Rn] D. Blasius, D. Ramakrishnan - Maass forms and Galois representations, à paraître dans Conf. on Galois groups and related topics, MSRI, mars 1987. Zbl0699.10043
  10. [B-Ro] D. Blasius, J. Rogawski - Galois representations for Hilbert modular forms, Bull. A.M.S., juillet 1989, 65-70. Zbl0684.12013MR983457
  11. [Bo 1] A. Borel - Stable cohomology of arithmetic groups, Ann. Scient. E.N.S.7, 1974, 235-272. Zbl0316.57026MR387496
  12. [Bo 2] A. Borel - Automorphic L-functions, in [PSPM], II, 27-72. Zbl0412.10017
  13. [Bo-J] A. Borel, H. Jacquet - Automorphic forms and automorphic representations, in [PSPM], I, 189-202. Zbl0414.22020MR546598
  14. [Bo-Wa] A. Borel, N. Wallach - Continuous cohomology, discrete subgroups and representations of reductive groups, Annals of Math. Studies94, Princeton University Press, 1980. Zbl0443.22010MR554917
  15. [Br-La] J.-L. Brylinski, J.-P. Labesse - Cohomologie d'intersection et fonctions L de certaines variétés de Shimura, Ann. Scient. E.N.S.17, 1984, 361-412. Zbl0553.12005MR777375
  16. [Ca 1] H. Carayol - Sur les représentations l-adiques attachées aux formes modulaires de Hilbert, Ann. Scient. E.N.S.19, 1986, 409-468. Zbl0616.10025MR870690
  17. [Ca 2] H. Carayol - Formes modulaires et représentations l-adiques, Astérisque147-148, 1987, 33-47. Zbl0629.14017MR891418
  18. [Ch-F] C.L. Chai, G. Faltings - Arithmetic compactification of Siegel moduli spaces and applications, prépublication 1988. 
  19. [Cl] L. Clozel - Motifs et formes automorphes : applications du principe de fonctorialité, prépublication 1989, à paraître dans Proc. of a conference on Shimura varieties, Ann Arbor, 1988. Zbl0705.11029MR1044819
  20. [Del] P. Deligne - Formes modulaires et représentations l-adiques, Sém. Bourbaki, exposé n° 355, Springer L.N.M.179, 1971, 139-172. Zbl0206.49901
  21. [De 2] P. Deligne - Non abelian class-field theory, in Mathematical developments arising from Hilbert problems, PSPM28, 1976, 41-43. 
  22. [De-Se] - P. Deligne, J.-P. Serre - Formes modulaires de poids 1, Ann. Scient. E.N.S.7, 1974, 507-530. Zbl0321.10026MR379379
  23. [F 1] G. Faltings - Arithmetic theory of Siegel modular forms, New York Number Theory Seminar, Springer L.N.M.1240, 1987, 101-108. Zbl0621.10018MR894507
  24. [F 2] G. Faltings - On the cohomology of locally symmetric hermitian spaces, Springer L.N.M.1029, 1984, 55-98. Zbl0539.22008MR732471
  25. [Ge] S. Gelbart - Automorphic forms on adele groups, Annals of Math. Studies83, Princeton University Press, 1975. Zbl0329.10018MR379375
  26. [Ge-Ja] S. Gelbart, H. Jacquet - A relation between automorphic forms on GL(2) and GL(3), Ann. Scient. E.N.S.11, 1978, 471-542. Zbl0406.10022MR533066
  27. [Ha 1] M. Harris - Arithmetic vector bundles and automorphic forms on Shimura varieties I, Inventiones Mathematicae82, 1985, 151-189 ; II, Compositio Mathematicae60, 1986, 323-378. Zbl0612.14019MR808114
  28. [Ha 2] M. Harris - Formes automorphes "géométriques" non holomorphes : problèmes d'arithméticité, in Séminaire de Théorie des Nombres de Paris, 1984-85, Progress in Math.63, BostonBirkhäuser, 1986, 109-129. Zbl0603.10030MR897345
  29. [Ha 3] M. Harris - Automorphie forms of ∂-cohomology type as coherent cohomology classes, à paraître dans Journal of Diff. Geom. Zbl0711.14012
  30. [Ha 4] M. HarrisAutomorphic forms and the cohomology of vector bundles on Shimura varieties, à paraître dans Proc. of a conference on Shimura varieties, Ann Arbor,1988. Zbl0716.14011
  31. [Ha-Ph] M. Harris, D.H. Phong - Cohomologie de Dolbeault à croissance logarithmique à l'infini, C.R.A.S. Paris302, 1986, 307-310. Zbl0597.32025MR838581
  32. [He] E. HeckeZur Theorie der elliptischen Modulfunktionen, n° 23, in Mathematische Werke, Vandenhoeck et Ruprecht, Göttingen, 1970, 2e édition. JFM52.0377.04
  33. [Hi] H. HidaGalois representations into GL2(Zp[[X]]) attached to ordinary cusp forms, Inv. Math.85, 1986, 546-613. Zbl0612.10021MR848685
  34. [Ja-La] H. Jacquet, R.P. Langlands - Automorphic forms on GL(2), Springer L.N.M.114, 1970. Zbl0236.12010MR401654
  35. [Ja-Sh] H. Jacquet, J. Shalika - Exterior square L-functions, à paraître dans Proc. of a conference on Shimura varieties, Ann Arbor, 1978. Zbl0695.10025
  36. [JPSS 1] H. Jacquet, I. Piatetski-Shapiro, J. Shalika - Converse theorem for GSp(4), en préparation. 
  37. [JPSS 2] H. Jacquet, I. Piatetski-Shapiro, J. Shalika - Rankin-Selberg convolutions, Amer. J. of Math.105, 1983, 367-464. Zbl0525.22018MR701565
  38. [Kn] A.W. Knapp - Representation theory of semisimple groups, Princeton Math. Series 36, 1986. Zbl0604.22001MR855239
  39. [Ko 1] R. Kottwitz - Shimura varietes and twisted orbital integrals, Math. Annalen269, 1984, 287-300. Zbl0533.14009MR761308
  40. [Ko 2] R. Kottwitz - On the λ-adic representations associated to some simple Shimura varieties, en préparation. Zbl0765.22011
  41. [Ku] Ph. Kutzko - The Langlands conjecture for GL2 of a local field, Annals of Math.112, 1980, 381-412. Zbl0469.22013MR592296
  42. [L-La] J.-P. Labesse, R.P. Langlands - L.-indistinguishability for SL(2), Can. J. Math.XXXI4, 1979, 726-785. Zbl0421.12014MR540902
  43. [La 1] R.P. Langlands - Problems in the theory of automorphic forms, in Lectures in modern analysis and applications III, Springer L.N.M.170, 1970, 19-61 Zbl0225.14022MR302614
  44. [La 2] R.P. Langlands - Modular forms and l-adic representations, in Modular functions of one variable II, Springer L.N.M.349, 1973, 361-500. Zbl0279.14007MR354617
  45. [La 3] R.P. Langlands - On the classification of irreducible representations of real algebraic groups, LA.S., Princeton, 1973. 
  46. [La 4] R.P. Langlands - On the zeta-functions of some simple Shimura varieties, Can. J. Math.31, 1979, 1121-1216. Zbl0444.14016MR553157
  47. [La 5] R.P. Langlands - Automorphic representations, Shimura varieties and motives, in Märchen in [PSPM] II, 205-246. Zbl0447.12009MR546619
  48. [La 6] R.P. Langlands - Base change for GL(2), Annals of Math. Studies96, Princeton University Press, 1980. Zbl0444.22007MR574808
  49. [La 7] R.P. Langlands - Les débuts d'une formule des traces stables, Pub. Math. Univ. ParisVII13, 1980. Zbl0532.22017
  50. [Ma 1] H. Maass - Über eine neue Art von nichtanalytischen automorphen Functionen und die Bestimmung Dirichletscher Reihen durch Fhnctional-gleichungen, Math. Annalen121, 1949, 141-183. Zbl0033.11702MR31519
  51. [Ma 2] H. Maass - Lectures on modular functions of one complex variable, Tata Lectures Notes29, Bombay,1983. Zbl0539.10021MR734485
  52. [Mi] J.S. Milne - Automorphic vector bundles on connected Shimura varieties, Invent. Math.92, 1987, 91-128. Zbl0684.14006MR931206
  53. [O] M. Ohta - On the zeta function of an abelian scheme over the Shimura curve, Japan J. Math.9, 1983, 1-26. Zbl0527.10023MR722534
  54. [PSPM] Automorphic functions, representations and L functions, Proc. Symp. Pure Math.33, Parts I and II, Providence, 1979. 
  55. [Ro] J. Rogawski - Automorphic representations of unitary groups in 3 variables, à paraître dans Annals of Math. Studies, Princeton University Press. Zbl0724.11031
  56. [Ro-Tu] J. Rogawski, J.B. Tunnell - On Artin L-functions associated to Hilbert modular forms of weight one, Inv. Math.74, 1983, 1-42. Zbl0523.12009MR722724
  57. [RZ] H. Reimann, T. Zink - Der Dieudonnémodul einer polarisierten abelschen Mannigfältigkeit von CM-Typ, Annals of Math.129, 1988, 461-482. Zbl0674.14030MR970608
  58. [Se] J.-P. Serre - Modular forms of weight one and Galois representations, in Algebraic Number Theory Field,Fröhlich ed., Academic Press, 1977, 193-268. Zbl0366.10022MR450201
  59. [Sh 1] G. Shimura - On modular correspondences for Sp(n, Z) and their congruence relations, Proc. N.A.S. USA49, 1963, 824-828. Zbl0122.08803MR157009
  60. [Sh 2] G. Shimura - On canonical models of arithmetic quotients of bounded symmetric domains I, Annals of Math.91, 1970, 144-222 ; II, Annals of Math.92, 1970, 528-549. Zbl0237.14010MR257031
  61. [Sh 3] G. Shimura - On the Fourier coefficients of modular forms of several variables, Nachr. Akad. Wiss. Göttingen17, 1975, 261-268. Zbl0332.32024MR485706
  62. [So] D. Soudry - The CAP representations of GSP(4, A), Journal de Crelle383, 1988, 87-108. Zbl0625.22013MR921988
  63. [Ta 1] R. Taylor - On congruences between modular forms, Thèse Princeton, 1988. 
  64. [Ta 2] R. Taylor - On Galois representations associated to Hibert modular forms, à paraître dans Invent. Math. Zbl0705.11031MR1016264
  65. [Ta 3] R. Taylor - Lettre à D. Blasius datée du 16.10.1988. 
  66. [Tt] J. Tate - Number theoretic background, in [PSPM] II, 3-26. MR546607
  67. [Tu] J.B. Tunnell - Artin's conjecture for representations of octahedral type, B. AMS5, 1981, 173-175. Zbl0475.12016MR621884
  68. [We] A. Weil - Dirichlet series and automorphic formsSpringer L.N.M., vol. 189, 1971. Zbl0218.10046
  69. [Wi 1] A. Wiles - On p-adic representations for totally real fields, Annals of Math.123, 1986, 407-456. Zbl0613.12013MR840720
  70. [Wi 2] A. Wiles - On ordinary λ-adic representations associated to modular forms, Invent. Math.94, 1988, 529-573. Zbl0664.10013
  71. [Wi 3] A. Wiles - The Iwasawa conjecture for totally real fields, prépublication, 1989. MR1053488
  72. [Wa] J.-L. Waldspurger - Représentation métaplectique et conjectures de Howe, Sém. Bourbaki, exposé n° 674, Astérisque152-153, 1987, 85-100. Zbl0634.10026MR936850

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