Formes non tempérées pour $U\left(3\right)$ et conjectures de Bloch-Kato

Bellaïche, Joël; Chenevier, Gaëtan

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 37 (2004) no. 4, pp. 611-662.

[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. | MR | Zbl

[2] Artin E., Tate J., Class Field Theory, Benjamin, 1968. | MR | Zbl

[3] Bellaïche J., Congruences endoscopiques et représentations galoisiennes, Thèse de l'université Paris 11, janvier 2002.

[4] Bellaïche J., À propos d'un lemme de Ribet, Rend. Sem. Univ. Padova 109 (2003) 47-62. | Numdam | MR | Zbl

[5] Bellaïche J., Graftieaux P., Représentations sur un anneau de valuation discrète complet, Math. Ann., à paraître. | MR | Zbl

[6] Bellaïche J., Graftieaux P., Augmentation du niveau pour $U\left(3\right)$, Preprint de l'université de Nice. | MR

[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. | Numdam | MR | Zbl

[8] Blasco L., Description du dual admissible de $U\left(2\text{,}1\right)\left(F\right)$ par la théorie des types de C. Bushnell et P. Kutzko, Manuscripta Math. 107 (2) (2002) 151-186. | MR | Zbl

[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. | MR | Zbl

[10] Blasius D., Rogawski J., Zeta functions of Shimura varieties, in: Motives, in: Proc. Sympos. Pure Math., vol. 55. | MR | Zbl

[11] Blasius D., Rogawski J., Motives for Hilbert modular forms, Invent. Math. 114 (1993) 55-87. | MR | Zbl

[12] Borel A., Some finiteness properties of adele groups over number fields, IHÉS Publ. Math. 16 (1963) 5-30. | Numdam | MR | Zbl

[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. | MR | Zbl

[14] Borel A., Casselman W., Automorphic forms, representations, and L-functions, in: Proc. Sympos. Pure Math., vol. 33, 1977, Corvallis. | Zbl

[15] Bosch S., Güntzer U., Remmert R., Non Archimedian Analysis, in: Grundlehren der mathematischen Wissenschaften, vol. 261, Springer-Verlag. | Zbl

[16] Bushnell C., Smooth representations of p-adic group, ICM 1998, pp. 770-779. | MR | Zbl

[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. | MR | Zbl

[18] Bushnell C., Kutzko P., Semi-simple types, Compositio Math. 119 (1999) 53-117. | Zbl

[19] Buzzard K., Eigenvarieties, 2002, en préparation.

[20] Cartier P., Representations of p-adic groups: a survey, in: Proc. Sympos. Pure Math., vol. 33, 1977, pp. 111-155, Part I. | MR | Zbl

[21] Casselman W., The unramified principal series of p-adic groups. I. The spherical function, Compositio Math. 40 (3) (1980) 387-406. | Numdam | MR | Zbl

[22] Chenevier G., Familles p-adiques de formes automorphes pour $GL\left(n\right)$, J. Reine Angew. Math. 570 (2004) 143-217. | MR | Zbl

[23] Chenevier G., Familles p-adiques de formes automorphes et applications aux conjectures de Bloch-Kato, Thèse de l'université Paris 7, 2003.

[24] Choucroun F., Analyse harmonique des groupes d'automorphismes d'arbres de Bruhat-Tits, Mém. Soc. Math. France (N.S.) (58) (1994) 170. | Numdam | MR | Zbl

[25] Clozel L., Représentations galoisiennes associées aux représentations automorphes autoduales de $GL\left(n\right)$, IHÉS Publ. Math. 73 (1991) 97-145. | Numdam | MR | Zbl

[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] Coleman R., P-adic Banach spaces & families of modular forms, Invent. Math. 127 (1997) 417-479. | MR | Zbl

[28] Curtis C., Reiner I., Representation Theory of Finite Groups and Associative Algebras, Wiley, 1962. | MR | Zbl

[29] Faltings G., Cristalline cohomology and p-adic Galois representations, in: Algebraic Analysis and Number Theory, JAMI Conference, 1988, pp. 25-90. | MR | Zbl

[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. | Numdam | MR | Zbl

[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. | Numdam | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[34] Harris M., On the local Langlands correspondence, in: Proceedings ICM 2002, vol. 2, 2002, pp. 583-597. | MR | Zbl

[35] Harris M., Taylor R., The Geometry and Cohomology of Some Simple Shimura Varieties, Ann. Math. Stud., vol. 151, 2001. | MR | Zbl

[36] Humphreys J.E., Reflection Groups and Coxeter Groups, Cambridge Studies in Advanced Mathematics, vol. 29. | Zbl

[37] Katz N., Messing W., Some consequences of the Riemann Hypothesis for varieties over finite fields, Invent. Math. 23 (1974) 73-77. | MR | Zbl

[38] Keys D., Principal series representations of special unitary groups over local fields, Compositio Math. 51 (1) (1984) 115-130. | Numdam | MR | Zbl

[39] Kisin M., Overconvergent modular forms and the Fontaine-Mazur conjecture, Invent. Math. 153 (2003) 363-454. | MR | Zbl

[40] Kottwitz R., Points on some Shimura varieties over finite fields, J. Amer. Math. Soc. 5 (2) (1992). | MR | Zbl

[41] Labesse J.-P., Cohomologie, stabilisation et changement de base, Astérisque, vol. 257, SMF, 1998. | Numdam | MR | Zbl

[42] Langlands R., Ramakhrisnan D. (Eds.), The Zeta Functions of Picard Modular Surfaces, Publications C.R.M., Montréal, 1992. | MR | Zbl

[43] Matsumura H., Commutative ring theory, Cambridge Studies in Adv. Math., vol. 8, 1980. | Zbl

[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. | MR | Zbl

[45] Motives, Proc. Sympos. Pure Math., vol. 55.

[46] Périodes p-adiques, Astérisque, vol. 223, Société mathématique de France, 1994. | Numdam | Zbl

[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. | Numdam | MR | Zbl

[48] Ribet K., A modular construction of unramified extensions of $Q\left({\zeta }_p\right)$, Invent. Math. 34 (3) (1976) 151-162. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[51] Rogawski J., On modules over the Hecke algebra of a p-adic group, Invent. Math. 79 (1985) 443-465. | MR | Zbl

[52] Rogawski J., Automorphic Representations of Unitary Groups in Three Variables, Ann. of Math. Stud., vol. 123, Princeton University Press, 1990. | MR | Zbl

[53] Rouquier R., Caractérisations des caractères et pseudo-caractères, J. Algebra 180 (1996) 571-586. | MR | Zbl

[54] Rubin K., The “main conjectures” of Iwasawa theory for imaginary quadratic fields, Invent. Math. 103 (1) (1991) 25-68. | Zbl

[55] Rubin K., Euler systems, Ann. of Math. Stud. 147 (2000). | MR | Zbl

[56] Serre J.-P., Endomorphismes complètement continus des espaces de Banach p-adiques, IHÉS Publ. Math. 12 (1962) 69-85. | Numdam | MR | Zbl

[57] Sen S., Continuous cohomology and p-adic Galois representations, Invent. Math. 62 (1980) 89-116. | MR | Zbl

[58] Sen S., An infinite dimensional Hodge-Tate theory, Bull. Soc. Math. France 121 (1993) 13-34. | Numdam | MR | Zbl

[59] Grothendieck A., Artin M., Verdier J.-L., Théorie des topos et cohomologie étale des schémas, Séminaire de géométrie algébrique IV, exposé XVI.

[60] Skinner C., Urban E., Sur les déformations p-adiques des formes de Saito-Kurokawa, C. R. Acad. Sci. Paris Sér. I 335 (2002) 581-586. | MR | Zbl

[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. | MR | Zbl

[62] Taylor R., Galois representations attached to Siegel modular forms of low weight, Duke Math. J. 63 (1991) 281-332. | MR | Zbl

[63] Tits J., Reductive groups over local fields, Part I, in: Proc. Sympos. Pure Math., vol. 33, 1977, pp. 29-69. | MR | Zbl

[64] Zelevinsky A.V., Induced representations of reductive p-adic groups II. On irreducible representations of $GL\left(n\right)$, Ann. Sci. École Norm. Sup. (4) 13 (1980) 165-210. | Numdam | MR | Zbl