Families of Galois representations and Selmer groups

Bellaïche, Joël ; Chenevier, Gaëtan

Astérisque, no. 324 (2009) , 326 p.

MR 2656025 | Zbl 1192.11035 | 3 citations dans Numdam

BibTeX
RIS

@book{AST_2009__324__R1_0,
     author = {Bella{\"\i}che, Jo\"el and Chenevier, Ga\"etan},
     title = {Families of {Galois} representations and {Selmer} groups},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {324},
     year = {2009},
     zbl = {1192.11035},
     mrnumber = {2656025},
     language = {en},
     url = {http://www.numdam.org/item/AST_2009__324__R1_0/}
}

TY  - BOOK
AU  - Bellaïche, Joël
AU  - Chenevier, Gaëtan
TI  - Families of Galois representations and Selmer groups
T3  - Astérisque
PY  - 2009
DA  - 2009///
IS  - 324
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/AST_2009__324__R1_0/
UR  - https://zbmath.org/?q=an%3A1192.11035
UR  - https://www.ams.org/mathscinet-getitem?mr=2656025
LA  - en
ID  - AST_2009__324__R1_0
ER  -

Bellaïche, Joël; Chenevier, Gaëtan. Families of Galois representations and Selmer groups. Astérisque, no. 324 (2009), 326 p. http://numdam.org/item/AST_2009__324__R1_0/

Bibliographie
Cité par

[1] "Périodes $p$ -adiques, Séminaire de Bures-sur-Yvette 1988" - Astérisque, vol. 223, 1994. | Zbl 0802.00019

[2] J. Adams & J. F. Johnson - "Endoscopic groups and packets of nontempered representations", Compositio Math. 64 (1987), p. 271-309. | EuDML 89877 | Numdam | MR 918414 | Zbl 0647.22008

[3] J. Arthur - "Unipotent automorphic representations : conjectures", Astérisque 171-172 (1989), p. 13-71. | Numdam | MR 1021499 | Zbl 0728.22014

[4] A. Ash & G. Stevens - " $p$ -adic deformations of cohomology classes of subgroups of $G L_{n} (ℤ)$ ", preprint. | MR 1464013 | Zbl 0866.20038

[5] J. Bellaïche - "Congruences endoscopiques et représentations galoisiennes", Ph.D. Thesis, Université Paris 11, 2002.

[6] J. Bellaïche, "À propos d'un lemme de Ribet", Rend. Sem. Mat. Univ. Padova 109 (2003), p. 45-62. | EuDML 108607 | Numdam | MR 1997986 | Zbl 1048.20032

[7] J. Bellaïche, "Sur la compatibilité entre les correspondances de Langlands locale et globale pour $U (3)$ ", Comment. Math. Helv. 81 (2006), p. 449-470. | Article | MR 2225634 | Zbl 1202.11033

[8] J. Bellaïche & G. Chenevier- "Formes non tempérées pour $U (3)$ et conjectures de Bloch-Kato", Ann. Sci. École Norm. Sup. 37 (2004), p. 611-662. | Article | EuDML 82641 | MR 2097894 | Zbl 1201.11051

[9] J. Bellaïche & G. Chenevier, "Lissité de la courbe de Hecke de $G L_{2}$ aux points Eisenstein critiques", J. Inst. Math. Jussieu 5 (2006), p. 333-349. | Article | MR 2225045 | Zbl 1095.11025

[10] J. Bellaïche & G. Chenevier, "Arbres et sous-groupes de $G L_{2}$ ", preprint.

[11] J. Bellaïche, G. Chenevier, C. Khare & M. Larsen - "Converging sequences of $p$ -adic Galois representations and density theorems", Int. Math. Res. Not. 2005 (2005), p. 3691-3720. | Article | MR 2200082 | Zbl 1091.11017

[12] J. Bellaïche & P. Graftieaux - "Représentations sur un anneau de valuation discrète complet", Math. Ann. 334 (2006), p. 465-488. | Article | MR 2207872 | Zbl 1178.20040

[13] L. Berger - "Représentations $p$ -adiques et équations différentielles", Invent. Math. 148 (2002), p. 219-284. | MR 1906150 | Zbl 1113.14016

[14] L. Berger, "Équations différentielles $p$ -adiques et $(φ, N)$ -modules filtrés", preprint. | MR 2493215 | Zbl 1168.11019

[15] N. Bergeron & L. Clozel - "Spectre automorphe des variétés hyperboliques et applications topologiques", Astérisque 303 (2005). | Numdam | MR 2245761 | Zbl 1098.11035

[17] J. N. Bernstein - "Le "centre" de Bernstein", in Representations of reductive groups over a local field, Travaux en Cours, Hermann, 1984, p. 1-32. | MR 771671 | Zbl 0599.22016

[18] J. N. Bernstein, " $P$ -invariant distributions on $G L (N)$ and the classification of unitary representations of $G L (N)$ (non-Archimedean case)", in Lie group representations, II (College Park, Md., 1982/1983), Lecture Notes in Math., vol. 1041, Springer, 1984, p. 50-102. | Article | MR 748505 | Zbl 0541.22009

[20] D. Blasius & J. D. Rogawski - "Tate classes and arithmetic quotients of the two-ball", in The zeta functions of Picard modular surfaces, Univ. Montréal, 1992, p. 421-444. | MR 1155236 | Zbl 0828.14012

[21] D. Blasius & J. D. Rogawski, "Motives for Hilbert modular forms", Invent. Math. 114 (1993), p. 55-87. | Article | EuDML 144142 | MR 1235020 | Zbl 0829.11028

[22] D. Blasius & J. D. Rogawski, "Zeta functions of Shimura varieties", in Motives (Seattle, WA, 1991), Proc. Sympos. Pure Math., vol. 55, Amer. Math. Soc, 1994, p. 525-571. | Article | MR 1265563 | Zbl 0827.11033

[23] S. Bloch & K. Kato - " $L$ -functions and Tamagawa numbers of motives", in The Grothendieck Festschrift, Vol. I, Progr. Math., vol. 86, Birkhäuser, 1990, p. 333-400. | MR 1086888 | Zbl 0768.14001

[24] A. Borel - "Some finiteness properties of adele groups over number fields", Publ. Math. I.H.É.S. 16 (1963), p. 5-30. | Article | EuDML 103836 | Numdam | MR 202718

[25] A. Borel, "Automorphic $L$ -functions", in Automorphic forms, representations and $L$ -functions, Proceedings of Symposia in Pure Mathematics, Oregon State Univ., Corvallis, Ore., 1977), vol. 33, Amer. Math. Soc, Providence, RI, 1979, p. 27-61. | MR 546608 | Zbl 0403.00002

[26] A. Borel & W. Casselman (eds.) - Automorphic forms, representations and $L$ -functions, Proceedings of Symposia in Pure Mathematics, vol. 33, 1979. | MR 546608 | Zbl 0403.00002

[27] S. Bosch, U. Güntzer & R. Remmert - Non-Archimedean analysis, Grund. Math. Wiss., vol. 261, Springer, 1984. | MR 746961 | Zbl 0539.14017

[28] N. Bourbaki - Éléments de mathématiques. Algèbre, Actualités Scientifiques et Industrielles, Hermann, 1961. | MR 271276 | Zbl 0108.04002

[29] N. Bourbaki, Éléments de mathématiques. Algèbre commutative, Actualités Scientifiques et Industrielles, Hermann, 1961. | Zbl 0108.04002

[30] C. Breuil & M. Emerton - "Représentations $p$ -adiques ordinaires de $G L_{2} (ℚ_{p})$ et compatibilité local-global", preprint I.H.É.S. | MR 3050714

[31] C. J. Bushnell & P. C. Kutzko - "Smooth representations of reductive $p$ -adic groups : structure theory via types", Proc. London Math. Soc. 77 (1998), p. 582-634. | Article | MR 1643417 | Zbl 0911.22014

[32] K. Buzzard - "Eigenvarieties", in $L$ -functions and Galois representations, London Math. Soc. Lecture Note Ser., vol. 320, Cambridge Univ. Press, 2007, p. 59-120. | Article | MR 2392353 | Zbl 1230.11054

[33] H. Carayol - "Formes modulaires et représentations galoisiennes à valeurs dans un anneau local complet", in $p$ -adic monodromy and the Birch and Swinnerton-Dyer conjecture (Boston, MA, 1991), Contemp. Math., vol. 165, Amer. Math. Soc.., 1994, p. 213-237. | Article | MR 1279611 | Zbl 0812.11036

[34] W. Casselman - "The unramified principal series of $𝔭$ -adic groups. I. The spherical function", Compositio Math. 40 (1980), p. 387-406. | EuDML 89444 | Numdam | MR 571057 | Zbl 0472.22004

[35] W. Casselman, "Introduction to the theory of admissible representations of $p$ -adic reductive groups", unpublished, http://www.math.ubc.ca/~cass/research/p-adic-book.dvi.

[36] G. Chenevier - "Familles p-adiques de formes automorphes pour $G L_{n}$ ", J. reine angew. Math. 570 (2004), p. 143-217. | MR 2075765 | Zbl 1093.11036

[37] G. Chenevier, "Une correspondance de Jacquet-Langlands $p$ -adique", Duke Math. J. 126 (2005), p. 161-194. | Article | MR 2111512 | Zbl 1070.11016

[38] G. Chenevier, "On number fields with given ramification", Compos. Math. 143 (2007), p. 1359-1373. | Article | MR 2371372

[39] G. Chenevier, "Quelques courbes de Hecke se plongent dans l'espace de Colmez", J. Number Theory 128 (2008), p. 2430-2449. | Article | MR 2394829 | Zbl 1235.11051

[41] L. Clozel, M. Harris & R. Taylor - "Automorphy for some $l$ -adic lifts of automorphic mod l representations", preprint. | Article | Numdam | MR 2470687 | Zbl 1169.11020

[42] R. F. Coleman - "Classical and overconvergent modular forms", Invent. Math. 124 (1996), p. 215-241. | Article | MR 1369416 | Zbl 0851.11030

[43] R. F. Coleman, " $p$ -adic Banach spaces and families of modular forms", Invent Math. 127 (1997), p. 417-479. | Article | MR 1431135 | Zbl 0918.11026

[44] R. F. Coleman & B. Mazur - "The eigencurve", in Galois representations in arithmetic algebraic geometry (Durham, 1996), London Math. Soc. Lecture Note Ser., vol. 254, Cambridge Univ. Press, 1998, p. 1-113. | MR 1696469 | Zbl 0932.11030

[45] P. Colmez - "Les conjectures de monodromie $p$ -adiques", Astérisque 290 (2003), p. 53-101, Séminaire Bourbaki, vol. 2001/2002, exposé n° 897. | EuDML 110314 | Numdam | MR 2074051 | Zbl 1127.12301

[46] P. Colmez, "Série principale unitaire pour $G L_{2} (ℚ_{p})$ et représentations triangulines de dimension $2$ ", preprint. people.math.jussieu.fr/~colmez/triangulines | MR 2642407

[48] B. Conrad, "Relative ampleness in rigid geometry", Ann. Inst. Fourier (Grenoble) 56 (2006), p. 1049-1126. | Article | EuDML 10167 | Numdam | Zbl 1125.14009

[49] C. W. Curtis & I. Reiner - Representation theory of finite groups and associative algebras, Pure and Applied Mathematics, Vol. XI, Interscience Publishers, a division of John Wiley & Sons, New York-London, 1962. | Zbl 0131.25601

[50] P. Deligne - "Les constantes des équations fonctionnelles des fonctions $L$ ", in Modular functions of one variable, II (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972), Springer , 1973, p. 501-597. Lecture Notes in Math., Vol. 349. | Article | Zbl 0271.14011

[51] J. Dieudonné - Sur les groupes classiques, Hermann, 1973, Troisième édition revue et corrigée, Publications de l'nstitut de Mathématique de l'Université de Strasbourg, VI, Actualités Scientifiques et Industrielles, No. 1040. | Zbl 0037.01304

[52] M. Emerton - "A local-global compatibility conjecture in the $p$ -adic Langlands programme for $G L_{2 / ℚ}$ ", Pure Appl. Math. Q. 2 (2006), p. 279-393. | Article | Zbl 1254.11106

[53] M. Emerton, "On the interpolation of systems of eigenvalues attached to automorphic Hecke eigenforms", Invent. Math. 164 (2006), p. 1-84. | Article | Zbl 1090.22008

[54] J.-M. Fontaine - "Représentations $p$ -adiques des corps locaux. I", in The Grothendieck Festschrift, Vol. II, Progr. Math., vol. 87, Birkhäuser, 1990, p. 249-309. | Zbl 0743.11066

[55] J.-M. Fontaine & B. Perrin-Riou - "Autour des conjectures de Bloch et Kato : cohomologie galoisienne et valeurs de fonctions $L$ ", in Motives (Seattle, WA, 1991), Proc. Sympos. Pure Math., vol. 55, Amer. Math. Soc., 1994, p. 599-706. | Article | Zbl 0821.14013

[56] M. Gerstenhaber - "On nilalgebras and linear varieties of nilpotent matrices. III", Ann. of Math. 70 (1959), p. 167-205. | Article | Zbl 0168.28103

[57] B. H. Gross - " $L$ -functions at the central critical point", in Motives (U. Jannsen, S. L. Kleiman & J-P. Serre, eds.), Proceedings of Symposia in Pure Mathematics, vol. 55. | Zbl 0807.14015

[58] G. Harder & R. Pink - "Modular konstruierte unverzweigte abelsche $p$ -Erweiterungen von $𝐐 (ζ_{p})$ und die Struktur ihrer Galoisgruppen", Math. Nachr. 159 (1992), p. 83-99. | Article | Zbl 0773.11069

[59] M. Harris - "Cohomological automorphic forms on unitary groups. II. Period relations and values of $L$ -functions", in Harmonic analysis, group representations, automorphic forms and invariant theory, Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap., vol. 12, World Sci. Publ., Hackensack, NJ, 2007, p. 89-149. | Zbl 1390.11088

[60] M. Harris et al. - "Stabilization of the trace formula, Shimura varieties, and arithmetic applications", book project of the GRFA seminar of Paris 7 university, http://www.institut.math.jussieu.fr/projets/fa/bp0.html. | Zbl 1255.11027

[61] M. Harris & J.-P. Labesse - "Conditional base change for unitary groups", Asian J. Math. 8 (2004), p. 653-683. | Article | Zbl 1071.22025

[62] M. Harris & R. Taylor - The geometry and cohomology of some simple Shimura varieties, Annals of Mathematics Studies, vol. 151, Princeton University Press, 2001. | Zbl 1036.11027

[63] R. Hartshorne - Algebraic geometry, Springer, 1977, Graduate Texts in Mathematics, No. 52. | Article | Zbl 0367.14001

[64] L. Herr - "Sur la cohomologie galoisienne des corps $p$ -adiques", Bull. Soc. Math. France 126 (1998), p. 563-600. | Article | EuDML 87795 | Numdam | Zbl 0967.11050

[65] H. Hida - $p$ -adic automorphic forms on Shimura varieties, Springer Monographs in Mathematics, Springer, 2004. | Article | Zbl 1055.11032

[66] J. Hoffstein & W. Luo - "Nonvanishing of L-series and the combinatorial sieve", Math. Res. Lett. 4 (1997), p. 435-444, with an appendix by David E. Rohrlich. | Article | Zbl 0893.11034

[67] N. Iwahori & H. Matsumoto - "On some Bruhat decomposition and the structure of the Hecke rings of $𝔭$ -adic Chevalley groups", Publ. Math. I.H.É.S. 25 (1965), p. 5-48. | Article | EuDML 103854 | Numdam | Zbl 0228.20015

[68] H. Jacquet & J. A. Shalika - "A non-vanishing theorem for zeta functions of $G L_{n}$ ", Invent. Math. 38 (1976/77), p. 1-16. | Article | EuDML 142439 | Zbl 0349.12006

[69] U. Jannsen, S. L. Kleiman & J-P. Serre (eds.) - Motives, Proceedings of Symposia in Pure Mathematics, vol. 55.

[70] K. Kato - "p-adic Hodge theory and values of zeta functions of modular forms", Astérisque 295 (2004), p. 117-290. | Numdam | Zbl 1142.11336

[71] K. S. Kedlaya - "A $p$ -adic local monodromy theorem", Ann. of Math. 160 (2004), p. 93-184. | Article | Zbl 1088.14005

[72] K. S. Kedlaya, "Slope fitrations revisited", Doc. Math. 10 (2005), p. 447-525. | EuDML 125591 | Zbl 1081.14028

[73] M. Kisin - "Overconvergent modular forms and the Fontaine-Mazur conjecture", Invent. Math. 153 (2003), p. 373-454. | Article | Zbl 1045.11029

[74] M. Kisin, "Geometric deformations of modular Galois representations", Invent. Math. 157 (2004), p. 275-328. | Article | Zbl 1150.11020

[75] T. Konno & K. Konno - "CAP automorphic representations of $U_{E / F}$ (4). I. Local $A$ -packets", preprint Kyushu University, 2003.

[76] J.-P. Labesse - "Cohomologie, stabilisation et changement de base", Astérisque 257 (1999). | Numdam | Zbl 1024.11034

[77] S. Lang - Algebra, Addison-Wesley Publishing Co., Inc., Reading, Mass., 1965. | Zbl 0712.00001

[78] R. P. Langlands & D. Ramakrishnan (eds.) - The zeta functions of Picard modular surfaces, Université de Montréal Centre de Recherches Mathématiques, 1992. | Zbl 0752.00024

[79] M. Lazard - "Les zéros des fonctions analytiques d'une variable sur un corps valué complet", Publ. Math. I.H.É.S. 14 (1962), p. 47-75. | Article | EuDML 103831 | Numdam

[80] R. Liu - "Cohomology and duality for $(ϕ, Γ)$ -modules over the Robba ring", Int. Math. Res. Not. 2008 (2008), Art. ID rnm150, 32. | Zbl 1248.11093

[81] I. G. Macdonald - Spherical functions on a group of $p$ -adic type, Ramanujan Institute, Centre for Advanced Study in Mathematics, University of Madras, Madras, 1971, Publications of the Ramanujan Institute, No. 2. | Zbl 0302.43018

[82] I. G. Macdonald, Symmetric functions and Hall polynomials, The Clarendon Press Oxford University Press, 1979, Oxford Mathematical Monographs. | Zbl 0487.20007

[83] H. Matsumura - Commutative ring theory, Cambridge Studies in Advanced Mathematics, vol. 8, Cambridge University Press, 1986. | Zbl 0603.13001

[84] B. Mazur - "An introduction to the deformation theory of Galois representations", in Modular forms and Fermat's last theorem (Boston, MA, 1995), Springer, 1997, p. 243-311. | Article | Zbl 0901.11015

[85] B. Mazur, "The theme of p-adic variation", in Mathematics : frontiers and perspectives, Amer. Math. Soc., 2000, p. 433-459. | Zbl 0959.14008

[86] B. Mazur & A. Wiles - "Class fields of abelian extensions of $𝐐$ ", Invent. Math. 76 (1984), p. 179-330. | Article | EuDML 143124 | Zbl 0545.12005

[87] C. Mœglin & J.-L. Waldspurger - "Le spectre résiduel de $G L (n)$ ", Ann. Sci. École Norm. Sup. 22 (1989), p. 605-674. | Article | EuDML 82264 | Numdam | Zbl 0696.10023

[88] S. Morel - "Étude de la cohomologie de certaines variétés de Shimura non compactes", preprint.

[89] J. Nekovář - "On the parity of ranks of Selmer groups. II", C. R. Acad. Sci. Paris Sér. I Math. 332 (2001), p. 99-104. | Article | Zbl 1090.11037

[90] J. Nekovář, "Selmer complexes", Astérisque 310 (2006). | Zbl 1211.11120

[91] L. Nyssen - "Pseudo-représentations", Math. Ann. 306 (1996), p. 257-283. | Article | EuDML 165454 | Zbl 0863.16012

[92] C. Procesi - "The invariant theory of $n \times n$ matrices", Advances in Math. 19 (1976), p. 306-381. | Article | Zbl 0331.15021

[93] C. Procesi, "A formal inverse to the Cayley-Hamilton theorem", J. Algebra 107 (1987), p. 63-74. | Article | Zbl 0618.16014

[94] M. Raynaud - Anneaux locaux henséliens, Lecture Notes in Math., Vol. 169, Springer, 1970. | Zbl 0203.05102

[95] M. Raynaud & L. Gruson - "Critères de platitude et de projectivité. Techniques de "platification" d'un module", Invent. Math. 13 (1971), p. 1-89. | Article | EuDML 142084 | Zbl 0227.14010

[96] K. A. Ribet - "A modular construction of unramified $p$ -extensions of $ℚ (μ_{p})$ ", Invent. Math. 34 (1976), p. 151-162. | Article | EuDML 142394 | Zbl 0338.12003

[97] F. Rodier - "Décomposition de la série principale des groupes réductifs $p$ -adiques", in Noncommutative harmonic analysis and Lie groups (Marseille, 1980), Lecture Notes in Math., vol. 880, Springer, 1981, p. 408-424. | Article | Zbl 0465.22009

[98] F. Rodier, "Decomposition of principal series for reductive $p$ -adic groups and the Langlands' classification", in Operator algebras and group representations, Vol. II (Neptun, 1980), Monogr. Stud. Math., vol. 18, Pitman, 1984, p. 86-94. | MR 733307 | Zbl 0553.12006

[99] J. D. Rogawski - Automorphic representations of unitary groups in three variables, Annals of Mathematics Studies, vol. 123, Princeton University Press, 1990. | MR 1081540 | Zbl 0724.11031

[100] J. D. Rogawski, "Analytic expression for the number of points mod $p$ ", in The zeta functions of Picard modular surfaces, Univ. Montréal, 1992, p. 65-109. | MR 1155227 | Zbl 0821.14015

[101] J. D. Rogawski, "The multiplicity formula for $A$ -packets", in The zeta functions of Picard modular surfaces, Univ. Montréal, 1992, p. 395-419. | MR 1155235 | Zbl 0823.11027

[102] R. Rouquier - "Caractérisation des caractères et pseudo-caractères", J. Algebra 180 (1996), p. 571-586. | Article | MR 1378546 | Zbl 0857.16013

[103] K. Rubin - "The "main conjectures" of Iwasawa theory for imaginary quadratic fields", Invent Math. 103 (1991), p. 25-68. | Article | EuDML 143852 | MR 1079839 | Zbl 0737.11030

[104] K. Rubin, Euler systems, Annals of Mathematics Studies, vol. 147, Princeton University Press, 2000. | MR 1749177 | Zbl 0977.11001

[105] P. Schneider - "Nonarchimedean functional analysis", Springer Monographs in Math., 2002. | Article | MR 1869547 | Zbl 0998.46044

[106] P. Schneider & E.-W. Zink - " $K$ -types for the tempered components of a $p$ -adic general linear group", J. reine angew. Math. 517 (1999), p. 161-208. | MR 1728541 | Zbl 0934.22021

[107] S. Sen - "Continuous cohomology and $p$ -adic Galois representations", Invent. Math. 62 (1980/81), p. 89-116. | Article | EuDML 142768 | MR 595584 | Zbl 0463.12005

[110] J-P. Serre, Corps locaux, Hermann, 1968, Deuxième édition, Publications de l'Université de Nancago, No. VIII. | MR 354618

[111] J-P. Serre, Cours d'arithmétique, P.U.F., 1970. | MR 255476 | Zbl 0225.12002

[112] C. Skinner & E. Urban - "Sur les déformations $p$ -adiques des formes de Saito-Kurokawa", C. R. Math. Acad. Sci. Paris 335 (2002), p. 581-586, a more detailed version appeared in [113]. | Article | MR 1941298 | Zbl 1024.11030

[113] C. Skinner & E. Urban, "Sur les déformations $p$ -adiques de certaines représentations automorphes", J. Inst. Math. Jussieu 5 (2006), p. 629-698. | Article | MR 2261226 | Zbl 1169.11314

[114] C. Skinner & E. Urban, "Vanishing of $L$ -functions and ranks of Selmer groups", in International Congress of Mathematicians. Vol. II, Eur. Math. Soc., Zürich, 2006, p. 473-500. | MR 2275606 | Zbl 1157.11020

[115] C. Soulé - "On higher $p$ -adic regulators", in Algebraic $K$ -theory, Evanston 1980 (Proc. Conf, Northwestern Univ., Evanston, Ill, 1980), Lecture Notes in Math., vol. 854, Springer, 1981, p. 372-401. | Article | MR 618313 | Zbl 0488.12008

[116] J. Tate - "Number theoretic background", in Automorphic forms, representations and $L$ -functions (Proc. Sympos. Pure Math., Oregon State Univ., Corval-lis, Ore., 1977), Part 2, Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., 1979, p. 3-26. | MR 546607 | Zbl 0422.12007

[117] R. Taylor - "Galois representations associated to Siegel modular forms of low weight", Duke Math. J. 63 (1991), p. 281-332. | MR 1115109 | Zbl 0810.11033

[118] R. Taylor & T. Yoshida - "Compatibility of local and global Langlands correspondences", J. Amer. Math. Soc. 20 (2007), p. 467-493. | Article | MR 2276777 | Zbl 1210.11118

[119] E. Urban - "On residually reducible representations on local rings", J. Algebra 212 (1999), p. 738-742. | Article | MR 1676863 | Zbl 0996.16007

[120] M.-F. Vignéras - Représentations $l$ -modulaires d'un groupe réductif $p$ -adique avec $l \neq p$ , Progress in Mathematics, vol. 137, Birkhäuser, 1996. | MR 1395151 | Zbl 0859.22001

[121] J.-L. Waldspurger - "Sur les coefficients de Fourier des formes modulaires de poids demi-entier", J. Math. Pures Appl. 60 (1981), p. 375-484. | MR 646366 | Zbl 0431.10015

[122] T. Weston - "Geometric Euler systems for locally isotropic motives", Compos. Math. 140 (2004), p. 317-332. | Article | MR 2027192 | Zbl 1133.11038

[123] A. Wiles - "The Iwasawa conjecture for totally real fields", Ann. of Math. 131 (1990), p. 493-540. | Article | MR 1053488 | Zbl 0719.11071

[124] A. Yamagami - "On $p$ -adic families of Hilbert cusp forms of finite slope", J. Number Theory 123 (2007), p. 363-387. | Article | MR 2301220 | Zbl 1160.11028