Formes de Maass et représentations galoisiennes

Henniart, Guy

Séminaire Bourbaki : volume 1988/89, exposés 700-714, Astérisque, no. 177-178 (1989), Exposé no. 711, 26 p.

corrigé par Erratum à l'exposé n°711 : « Formes de Maass et représentations galoisiennes »

MR Zbl

@incollection{SB_1988-1989__31__277_0,
     author = {Henniart, Guy},
     title = {Formes de {Maass} et repr\'esentations galoisiennes},
     booktitle = {S\'eminaire Bourbaki : volume 1988/89, expos\'es 700-714},
     series = {Ast\'erisque},
     note = {talk:711},
     pages = {277--302},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {177-178},
     year = {1989},
     mrnumber = {1040577},
     zbl = {0703.11062},
     language = {fr},
     url = {http://www.numdam.org/item/SB_1988-1989__31__277_0/}
}

TY  - CHAP
AU  - Henniart, Guy
TI  - Formes de Maass et représentations galoisiennes
BT  - Séminaire Bourbaki : volume 1988/89, exposés 700-714
AU  - Collectif
T3  - Astérisque
N1  - talk:711
PY  - 1989
SP  - 277
EP  - 302
IS  - 177-178
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/SB_1988-1989__31__277_0/
LA  - fr
ID  - SB_1988-1989__31__277_0
ER  -

%0 Book Section
%A Henniart, Guy
%T Formes de Maass et représentations galoisiennes
%B Séminaire Bourbaki : volume 1988/89, exposés 700-714
%A Collectif
%S Astérisque
%Z talk:711
%D 1989
%P 277-302
%N 177-178
%I Société mathématique de France
%U http://www.numdam.org/item/SB_1988-1989__31__277_0/
%G fr
%F SB_1988-1989__31__277_0

Henniart, Guy. Formes de Maass et représentations galoisiennes, dans Séminaire Bourbaki : volume 1988/89, exposés 700-714, Astérisque, no. 177-178 (1989), Exposé no. 711, 26 p. http://www.numdam.org/item/SB_1988-1989__31__277_0/

Bibliographie
Cité par

[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. | MR | Zbl

[Ar 2] J. Arthur - On a family of distributions obtained from orbits, Can. J. Math. 38, 1986, 179-214. | MR | Zbl

[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. | MR | Zbl

[AMRT] A. Ash, D. Mumford, M. Rapoport, Y.-S. Tai - Smooth compactifcation of locally symmetric varieties, Brooklin, Mass. Math. Sci. Press, 1975. | MR | Zbl

[Bl] D. Blasius - Automorphic forms and Galois representations : some examples, à paraître dans Proc. of a conference on Shimura varieties, Ann Arbor, 1988. | Zbl

[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. Paris 305, 1987, 705-708. | MR | Zbl

[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. Paris 306, 1988, 59-62. | MR | Zbl

[BHR] D. Blasius, M. Harris, D. Ramakrishnan - Coherent cohomology, limits of discrete series and Maass forms of Galois type, notes préliminaires.

[B-Rn] D. Blasius, D. Ramakrishnan - Maass forms and Galois representations, à paraître dans Conf. on Galois groups and related topics, MSRI, mars 1987. | Zbl

[B-Ro] D. Blasius, J. Rogawski - Galois representations for Hilbert modular forms, Bull. A.M.S., juillet 1989, 65-70. | MR | Zbl

[Bo 1] A. Borel - Stable cohomology of arithmetic groups, Ann. Scient. E.N.S. 7, 1974, 235-272. | Numdam | MR | Zbl

[Bo 2] A. Borel - Automorphic L-functions, in [PSPM], II, 27-72. | Zbl

[Bo-J] A. Borel, H. Jacquet - Automorphic forms and automorphic representations, in [PSPM], I, 189-202. | MR | Zbl

[Bo-Wa] A. Borel, N. Wallach - Continuous cohomology, discrete subgroups and representations of reductive groups, Annals of Math. Studies 94, Princeton University Press, 1980. | MR | Zbl

[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. | Numdam | MR | Zbl

[Ca 1] H. Carayol - Sur les représentations l-adiques attachées aux formes modulaires de Hilbert, Ann. Scient. E.N.S. 19, 1986, 409-468. | Numdam | MR | Zbl

[Ca 2] H. Carayol - Formes modulaires et représentations l-adiques, Astérisque 147-148, 1987, 33-47. | Numdam | MR | Zbl

[Ch-F] C. L. Chai, G. Faltings - Arithmetic compactification of Siegel moduli spaces and applications, prépublication 1988.

[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. | MR | Zbl

[Del] P. Deligne - Formes modulaires et représentations l-adiques, Sém. Bourbaki, exposé n° 355, Springer L.N.M. 179, 1971, 139-172. | Numdam | Zbl

[De 2] P. Deligne - Non abelian class-field theory, in Mathematical developments arising from Hilbert problems, PSPM 28, 1976, 41-43.

[De-Se] - P. Deligne, J.-P. Serre - Formes modulaires de poids 1, Ann. Scient. E.N.S. 7, 1974, 507-530. | Numdam | MR | Zbl

[F 1] G. Faltings - Arithmetic theory of Siegel modular forms, New York Number Theory Seminar, Springer L.N.M. 1240, 1987, 101-108. | MR | Zbl

[F 2] G. Faltings - On the cohomology of locally symmetric hermitian spaces, Springer L.N.M. 1029, 1984, 55-98. | MR | Zbl

[Ge] S. Gelbart - Automorphic forms on adele groups, Annals of Math. Studies 83, Princeton University Press, 1975. | MR | Zbl

[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. | Numdam | MR | Zbl

[Ha 1] M. Harris - Arithmetic vector bundles and automorphic forms on Shimura varieties I, Inventiones Mathematicae 82, 1985, 151-189 ; II, Compositio Mathematicae 60, 1986, 323-378. | Numdam | MR | Zbl

[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, Boston Birkhäuser, 1986, 109-129. | MR | Zbl

[Ha 3] M. Harris - Automorphie forms of ∂-cohomology type as coherent cohomology classes, à paraître dans Journal of Diff. Geom. | Zbl

[Ha 4] M. Harris Automorphic forms and the cohomology of vector bundles on Shimura varieties, à paraître dans Proc. of a conference on Shimura varieties, Ann Arbor,1988. | Zbl

[Ha-Ph] M. Harris, D. H. Phong - Cohomologie de Dolbeault à croissance logarithmique à l'infini, C.R.A.S. Paris 302, 1986, 307-310. | MR | Zbl

[He] E. Hecke Zur Theorie der elliptischen Modulfunktionen, n° 23, in Mathematische Werke, Vandenhoeck et Ruprecht, Göttingen, 1970, 2e édition. | JFM

[Hi] H. Hida Galois representations into GL2(Zp[[X]]) attached to ordinary cusp forms, Inv. Math. 85, 1986, 546-613. | MR | Zbl

[Ja-La] H. Jacquet, R. P. Langlands - Automorphic forms on GL(2), Springer L.N.M. 114, 1970. | MR | Zbl

[Ja-Sh] H. Jacquet, J. Shalika - Exterior square L-functions, à paraître dans Proc. of a conference on Shimura varieties, Ann Arbor, 1978. | Zbl

[JPSS 1] H. Jacquet, I. Piatetski-Shapiro, J. Shalika - Converse theorem for GSp(4), en préparation.

[JPSS 2] H. Jacquet, I. Piatetski-Shapiro, J. Shalika - Rankin-Selberg convolutions, Amer. J. of Math. 105, 1983, 367-464. | MR | Zbl

[Kn] A. W. Knapp - Representation theory of semisimple groups, Princeton Math. Series 36, 1986. | MR | Zbl

[Ko 1] R. Kottwitz - Shimura varietes and twisted orbital integrals, Math. Annalen 269, 1984, 287-300. | MR | Zbl

[Ko 2] R. Kottwitz - On the λ-adic representations associated to some simple Shimura varieties, en préparation. | Zbl

[Ku] Ph. Kutzko - The Langlands conjecture for GL2 of a local field, Annals of Math. 112, 1980, 381-412. | MR | Zbl

[L-La] J.-P. Labesse, R. P. Langlands - L.-indistinguishability for SL(2), Can. J. Math. XXXI 4, 1979, 726-785. | MR | Zbl

[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 | MR | Zbl

[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. | MR | Zbl

[La 3] R. P. Langlands - On the classification of irreducible representations of real algebraic groups, LA.S., Princeton, 1973.

[La 4] R. P. Langlands - On the zeta-functions of some simple Shimura varieties, Can. J. Math. 31, 1979, 1121-1216. | MR | Zbl

[La 5] R. P. Langlands - Automorphic representations, Shimura varieties and motives, in Märchen in [PSPM] II, 205-246. | MR | Zbl

[La 6] R. P. Langlands - Base change for GL(2), Annals of Math. Studies 96, Princeton University Press, 1980. | MR | Zbl

[La 7] R. P. Langlands - Les débuts d'une formule des traces stables, Pub. Math. Univ. Paris VII 13, 1980. | Zbl

[Ma 1] H. Maass - Über eine neue Art von nichtanalytischen automorphen Functionen und die Bestimmung Dirichletscher Reihen durch Fhnctional-gleichungen, Math. Annalen 121, 1949, 141-183. | MR | Zbl

[Ma 2] H. Maass - Lectures on modular functions of one complex variable, Tata Lectures Notes 29, Bombay,1983. | MR | Zbl

[Mi] J. S. Milne - Automorphic vector bundles on connected Shimura varieties, Invent. Math. 92, 1987, 91-128. | MR | Zbl

[O] M. Ohta - On the zeta function of an abelian scheme over the Shimura curve, Japan J. Math. 9, 1983, 1-26. | MR | Zbl

[PSPM] Automorphic functions, representations and L functions, Proc. Symp. Pure Math. 33, Parts I and II, Providence, 1979.

[Ro] J. Rogawski - Automorphic representations of unitary groups in 3 variables, à paraître dans Annals of Math. Studies, Princeton University Press. | Zbl

[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. | MR | Zbl

[RZ] H. Reimann, T. Zink - Der Dieudonnémodul einer polarisierten abelschen Mannigfältigkeit von CM-Typ, Annals of Math. 129, 1988, 461-482. | MR | Zbl

[Se] J.-P. Serre - Modular forms of weight one and Galois representations, in Algebraic Number Theory Field,Fröhlich ed., Academic Press, 1977, 193-268. | MR | Zbl

[Sh 1] G. Shimura - On modular correspondences for Sp(n, Z) and their congruence relations, Proc. N.A.S. USA 49, 1963, 824-828. | MR | Zbl

[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. | MR | Zbl

[Sh 3] G. Shimura - On the Fourier coefficients of modular forms of several variables, Nachr. Akad. Wiss. Göttingen 17, 1975, 261-268. | MR | Zbl

[So] D. Soudry - The CAP representations of GSP(4, A), Journal de Crelle 383, 1988, 87-108. | MR | Zbl

[Ta 1] R. Taylor - On congruences between modular forms, Thèse Princeton, 1988.

[Ta 2] R. Taylor - On Galois representations associated to Hibert modular forms, à paraître dans Invent. Math. | MR | Zbl

[Ta 3] R. Taylor - Lettre à D. Blasius datée du 16.10.1988.

[Tt] J. Tate - Number theoretic background, in [PSPM] II, 3-26. | MR

[Tu] J. B. Tunnell - Artin's conjecture for representations of octahedral type, B. AMS 5, 1981, 173-175. | MR | Zbl

[We] A. Weil - Dirichlet series and automorphic forms Springer L.N.M., vol. 189, 1971. | Zbl

[Wi 1] A. Wiles - On p-adic representations for totally real fields, Annals of Math. 123, 1986, 407-456. | MR | Zbl

[Wi 2] A. Wiles - On ordinary λ-adic representations associated to modular forms, Invent. Math. 94, 1988, 529-573. | Zbl

[Wi 3] A. Wiles - The Iwasawa conjecture for totally real fields, prépublication, 1989. | MR

[Wa] J.-L. Waldspurger - Représentation métaplectique et conjectures de Howe, Sém. Bourbaki, exposé n° 674, Astérisque 152-153, 1987, 85-100. | Numdam | MR | Zbl