Invariant $L$ et série spéciale $p$-adique

Breuil, Christophe

Annales scientifiques de l'École Normale Supérieure, Tome 37 (2004), p. 559-610 / Harvested from Numdam

Détail

Publié le : 2004-01-01

Zbl 02165093 | 1 citation dans Numdam

DOI : https://doi.org/10.1016/j.ansens.2004.02.001

Bibliographie

[1] Barthel L., Livné R., Modular representations of ${\mathrm {GL}}_{2}$ of a local field: the ordinary, unramified case, J. Number Theory 55 (1995) 1-27. | MR 1361556 | Zbl 0841.11026

[2] Barthel L., Livné R., Irreducible modular representations of ${\mathrm {GL}}_{2}$ of a local field, Duke Math. J. 75 (1994) 261-292. | MR 1290194 | Zbl 0826.22019

[3] Bertolini M., Darmon H., Iovita A., Spiess M., Teitelbaum's exceptional zero conjecture in the anticyclotomic setting, Amer. J. Math. 124 (2002) 411-449. | MR 1890998 | Zbl 1079.11036

[4] Breuil C., Intégration p-adique, in: Séminaire Bourbaki 860, Astérisque, vol. 266, 2000, pp. 319-350. | Numdam | MR 1772678 | Zbl 1015.11028

[5] Breuil C., p-adic Hodge theory, deformations and local Langlands, cours au C.R.M. de Barcelone, juillet 2001, disponible à l'adresse, http://www.math.u-psud.fr/~breuil/.

[6] Breuil C., Sur quelques représentations modulaires et p-adiques de ${\mathrm {GL}}_{2}\left({Q}_{p}\right)$ I, Comp. Math. 138 (2003) 165-188. | MR 2018825 | Zbl 1044.11041

[7] Breuil C., Sur quelques représentations modulaires et p-adiques de ${\mathrm {GL}}_{2}\left({Q}_{p}\right)$ II, J. Institut Math. Jussieu 2 (2003) 23-58. | MR 1955206 | Zbl 02011912

[8] Breuil C., Série spéciale p-adique et cohomologie étale complétée, prépublication I.H.É.S., 2003, disponible à l'adresse, http://www.ihes.fr/~breuil/publications.html.

[9] Breuil C., Mézard A., Multiplicités modulaires et représentations de ${\mathrm {GL}}_{2}\left({Z}_{p}\right)$ et de $\mathrm {Gal}({\overline{Q}}_{p}/{Q}_{p})$ en $\ell =p$, Duke Math. J. 115 (2002) 205-310. | MR 1944572 | Zbl 1042.11030

[10] Coleman R., A p-adic Shimura isomorphism and p-adic periods of modular forms, Contemp. Math. 165 (1994) 21-51. | MR 1279600 | Zbl 0838.11033

[11] Colmez P., Fontaine J.-M., Construction des représentations p-adiques semi-stables, Invent. Math. 140 (2000) 1-43. | MR 1779803 | Zbl 1010.14004

[12] Deligne P., Formes modulaires et représentations de ${\mathrm {GL}}_{2}$, in: Modular Functions of One Variable II, Lecture Notes, vol. 349, 1973, pp. 55-105. | MR 347738 | Zbl 0271.10032

[13] Deligne P., Serre J.-P., Formes modulaires de poids 1, Ann. Sci. E.N.S. 7 (1974) 507-530. | Numdam | MR 379379 | Zbl 0321.10026

[14] Emerton M., On the interpolation of systems of eigenvalues attached to automorphic Hecke eigenforms, prépublication 2003.

[15] Féaux De Lacroix C.T., Einige Resultate über die topologischen Darstellungen p-adischer Liegruppen auf unendlich dimensionalen Vektorräumen über einem p-adischen Körper, in: Schriftenreihe Math. Univ. Münster, 3. Serie, Heft 23, 1999, pp. 1-111. | MR 1691735 | Zbl 0963.22009

[16] Fontaine J.-M., Représentations ℓ-adiques potentiellement semi-stables, in: Astérisque, vol. 223, Soc. Math. France, 1994, pp. 321-347. | MR 1293977 | Zbl 0873.14020

[17] Grosse-Klönne E., Integral structures in automorphic line bundles on the p-adic upper half plane, Math. Annalen 329 (2004) 463-493. | MR 2127986 | Zbl 1087.11029

[18] Iovita A., Spiess M., Derivatives of p-adic L-functions, Heegner cycles and monodromy modules attached to modular forms, Invent. Math. 154 (2003) 333-384. | MR 2013784 | Zbl 1099.11032

[19] Mazur B., On monodromy invariants occurring in global arithmetic, and Fontaine's theory, in: Contemp. Math., vol. 165, 1994, pp. 1-20. | MR 1279599 | Zbl 0846.11039

[20] Mazur B., Tate J., Teitelbaum J., On p-adic analogues of the conjectures of Birch and Swinnerton-Dyer, Invent. Math. 84 (1986) 1-48. | MR 830037 | Zbl 0699.14028

[21] Morita Y., A p-adic theory of hyperfunctions I, Publ. R.I.M.S. 17 (1981) 1-24. | MR 613933 | Zbl 0457.12010

[22] Morita Y., Analytic representations of ${\mathrm {SL}}_{2}$ over a $p$-adic number field II, in: Prog. Math., vol. 46, Birkhäuser, 1984, pp. 282-297. | MR 763019 | Zbl 0549.22008

[23] Saito T., Modular forms and p-adic Hodge theory, Invent. Math. 129 (1997) 607-620. | MR 1465337 | Zbl 0877.11034

[24] Schneider P., Nonarchimedean Functional Analysis, Springer-Verlag, 2001. | MR 1869547 | Zbl 0998.46044

[25] Schneider P., Teitelbaum J., Locally analytic distributions and p-adic representation theory, with applications to ${\mathrm {GL}}_{2}$, J. Amer. Math. Soc. 15 (2002) 443-468. | MR 1887640 | Zbl 1028.11071

[26] Schneider P., Teitelbaum J., $U\left(g\right)$-finite locally analytic representations, Representation Theory 5 (2001) 111-128. | MR 1835001 | Zbl 1028.17007

[27] Schneider P., Teitelbaum J., Banach space representations and Iwasawa theory, Israel J. Math. 127 (2002) 359-380. | MR 1900706 | Zbl 1006.46053

[28] Schneider P., Teitelbaum J., p-adic boundary values, in: Astérisque, vol. 278, Soc. Math. France, 2002, pp. 51-125. | MR 1922824 | Zbl 1051.14024

[29] Schneider P., Teitelbaum J., Algebras of p-adic distributions and admissible representations, Invent. Math. 153 (2003) 145-196. | MR 1990669 | Zbl 1028.11070

[30] De Shalit E., Eichler cohomology and periods of modular forms on p-adic Schottky groups, J. Reine Angew. Math. 400 (1989) 3-31. | MR 1013723 | Zbl 0674.14031

[31] Shimura G., Introduction to the Arithmetic Theory of Automorphic Functions, Princeton University Press, Mathematical Society of Japan. | MR 1291394 | Zbl 0221.10029

[32] Teitelbaum J., Values of p-adic L-functions and a p-adic Poisson kernel, Invent. Math. 101 (1990) 395-410. | MR 1062968 | Zbl 0731.11065

[33] Teitelbaum J., Modular representations of ${\mathrm {PGL}}_{2}$ and automorphic forms for Shimura curves, Invent. Math. 113 (1993) 561-580. | MR 1231837 | Zbl 0806.11027

[34] Vignéras M.-F., Arithmétique des algèbres de quaternions, Lecture Notes in Math., vol. 800, Springer, 1980. | MR 580949 | Zbl 0422.12008