Représentations $p$-adiques ordinaires de $\mathbf{GL}_2 (\mathbf{Q}

Représentations

p

-adiques ordinaires de

{𝐆𝐋}_{2} (𝐐_{p})

et compatibilité local-global

Breuil, Christophe ; Emerton, Matthew

Représentations

p

-adiques de groupes

p

-adiques III : méthodes globales et géométriques, Astérisque, no. 331 (2010), pp. 255-315.

MR Zbl | 7 citations dans Numdam

@incollection{AST_2010__331__255_0,
     author = {Breuil, Christophe and Emerton, Matthew},
     title = {Repr\'esentations $p$-adiques ordinaires de $\mathbf{GL}_2 (\mathbf{Q}_p)$ et compatibilit\'e local-global},
     booktitle = {Repr\'esentations $p$-adiques de groupes $p$-adiques III : m\'ethodes globales et g\'eom\'etriques},
     series = {Ast\'erisque},
     pages = {255--315},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {331},
     year = {2010},
     mrnumber = {2667890},
     zbl = {1251.11043},
     language = {fr},
     url = {http://www.numdam.org/item/AST_2010__331__255_0/}
}

TY  - CHAP
AU  - Breuil, Christophe
AU  - Emerton, Matthew
TI  - Représentations $p$-adiques ordinaires de $\mathbf{GL}_2 (\mathbf{Q}_p)$ et compatibilité local-global
BT  - Représentations $p$-adiques de groupes $p$-adiques III : méthodes globales et géométriques
AU  - Collectif
T3  - Astérisque
PY  - 2010
SP  - 255
EP  - 315
IS  - 331
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/AST_2010__331__255_0/
LA  - fr
ID  - AST_2010__331__255_0
ER  -

%0 Book Section
%A Breuil, Christophe
%A Emerton, Matthew
%T Représentations $p$-adiques ordinaires de $\mathbf{GL}_2 (\mathbf{Q}_p)$ et compatibilité local-global
%B Représentations $p$-adiques de groupes $p$-adiques III : méthodes globales et géométriques
%A Collectif
%S Astérisque
%D 2010
%P 255-315
%N 331
%I Société mathématique de France
%U http://www.numdam.org/item/AST_2010__331__255_0/
%G fr
%F AST_2010__331__255_0

Breuil, Christophe; Emerton, Matthew. Représentations $p$-adiques ordinaires de $\mathbf{GL}_2 (\mathbf{Q}_p)$ et compatibilité local-global, dans Représentations $p$-adiques de groupes $p$-adiques III : méthodes globales et géométriques, Astérisque, no. 331 (2010), pp. 255-315. http://www.numdam.org/item/AST_2010__331__255_0/

Bibliographie
Cité par

[1] Y. Amice & J. Vélu - Distributions $p$ -adiques associées aux séries de Hecke, Astérisque 24-25 (1975), p. 119-131. | Numdam | MR | Zbl

[2] F. Baldassarri & B. Chiarellotto - Algebraic versus rigid cohomology with logarithmic coefficients, in Barsotti Symposium in Algebraic Geometry (Abano Terme, 1991), Perspect. Math., vol. 15, Academic Press, 1994, p. 11-50. | DOI | MR | Zbl

[3] L. Berger & C. Breuil - Sur quelques représentations potentiellement cristallines de $G L_{2} (𝐐_{p})$ , Astérisque 330 (2010), p. 155-211. | Numdam | MR | Zbl

[4] L. Berger & C. Breuil - Towards a $p$ -adic langlands programme, cours au C.M.S. de Hangzhou (2004) http://www.ihes.fr/~breuil/publications.html.

[5] P. Berthelot - Cohomologie rigide et cohomologie rigide à support propre. Première partie, http://www.maths.univ-rennesl.fr/~berthelo/.

[6] N. Bourbaki - Topological vector spaces. Chapters 1-5, Elements of Mathematics (Berlin), Springer, 1987. | MR | Zbl

[7] C. Breuil - Sur quelques representations modulaires et $p$ -adiques de ${𝐆𝐋}_{2} (𝐐_{p})$ . II, J. Inst. Math. Jussieu 2 (2003), p. 23-58. | DOI | MR | Zbl

[8] C. Breuil - Invariant $ℒ$ et série spéciale $p$ -adique, Ann. Sci. École Norm. Sup. 37 (2004), p. 559-610. | DOI | EuDML | Numdam | MR | Zbl

[9] C. Breuil - Série spéciale $p$ -adique et cohomologie étale complétée, ce volume. | Numdam | Zbl

[10] K. Buzzard & F. Calegari - Slopes of overconvergent $2$ -adic modular forms, Compos. Math. 141 (2005), p. 591-604. | DOI | MR | Zbl

[11] K. Buzzard & R. Taylor - Companion forms and weight one forms, Ann. of Math. 149 (1999), p. 905-919. | DOI | EuDML | MR | Zbl

[12] R. F. Coleman - A $p$ -adic Shimura isomorphism and $p$ -adic periods of modular forms, in $p$ -adic monodromy and the Birch and Swinnerton-Dyer conjecture (Boston, MA, 1991), Contemp. Math., vol. 165, Amer. Math. Soc. 1994, p. 21-51. | DOI | MR | Zbl

[13] R. F. Coleman - Classical and overconvergent modular forms, Invent. Math. 124 (1996), p. 215-241. | DOI | MR | Zbl

[14] R. F. Coleman - Classical and overconvergent modular forms of higher level, J. Théor. Nombres Bordeaux 9 (1997), p. 395-403. | DOI | EuDML | Numdam | MR | Zbl

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

[16] R. F. Coleman & A. Iovita - Hidden structures on semi-stable curves, ce volume. | Numdam | Zbl

[17] 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 | Zbl

[18] P. Colmez - Une correspondance de Langlands $p$ -adique pour les représentations semi-stables de dimension $2$ , prépublication, 2004.

[19] P. Colmez - La série principale unitaire de ${𝐆𝐋}_{2} (𝐐_{p})$ , Astérisque 330 (2010), p. 213-262. | Numdam | MR | Zbl

[20] P. Deligne - Formes modulaires et représentations de $G L (2)$ , in Modular functions of one variable, II (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972), Springer, 1973, p. 55-105. Lecture Notes in Math., Vol. 349. | DOI | MR | Zbl

[21] M. Emerton - $p$ -adic $L$ -functions and unitary completions of representations of $p$ -adic reductive groups, Duke Math. J. 130 (2005), p. 353-392. | MR | Zbl

[22] M. Emerton - Jacquet modules of locally analytic representations of $p$ -adic reductive groups. I. Construction and first properties, Ann. Sci. École Norm. Sup. 39 (2006), p. 775-839. | DOI | EuDML | Numdam | MR | Zbl

[23] M. Emerton - A local-global compatibility conjecture in the $p$ -adic Langlands programme for ${𝐆𝐋}_{2 / ℚ}$ , Pure Appl. Math. Q. 2 (2006), p. 279-393. | DOI | MR | Zbl

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

[25] M. Emerton - Jacquet modules of locally analytic representations of $p$ -adic reductive groups II. The relation to parabolic induction, à paraître dans J. Institut Math. Jussieu.

[26] M. Emerton - Locally analytic vectors in representations of locally $p$ -adic analytic groups, à paraître dans Memoirs of the AMS.

[27] G. Faltings - Crystalline cohomology of semistable curve-the $𝐐_{p}$ -theory, J. Algebraic Geom. 6 (1997), p. 1-18. | MR | Zbl

[28] G. Faltings - Almost étale extensions, Astérisque 279 (2002), p. 185-270. | Numdam | MR | Zbl

[29] G. Faltings & B. W. Jordan - Crystalline cohomology and $G L (2, 𝐐)$ , Israel J. Math. 90 (1995), p. 1-66. | DOI | MR | Zbl

[30] E. Ghate - Ordinary forms and their local Galois representations, à paraître dans les Actes de la conférence à Hyderabad 2003. | Zbl

[31] E. Ghate & A. Mézard - Filtered modules attached to modular forms, prépublication, 2006.

[32] F. Q. Gouvêa - Arithmetic of $p$ -adic modular forms, Lecture Notes in Math., vol. 1304, Springer, 1988. | MR | Zbl

[33] B. H. Gross - A tameness criterion for Galois representations associated to modular forms (mod $p$ ), Duke Math. J. 61 (1990), p. 445-517. | DOI | MR | Zbl

[34] H. Hida - Galois representations into $G L_{2} (𝐙_{p} [[X]])$ attached to ordinary cusp forms, Invent. Math. 85 (1986), p. 545-613. | DOI | EuDML | MR | Zbl

[35] N. M. Katz - $p$ -adic properties of modular schemes and modular forms, in Modular functions of one variable, III (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972), Springer, 1973, p. 69-190. Lecture Notes in Mathematics, Vol. 350. | DOI | MR | Zbl

[36] N. M. Katz & B. Mazur - Arithmetic moduli of elliptic curves, Annals of Math. Studies, vol. 108, Princeton Univ. Press, 1985. | MR | Zbl

[37] M. Kurihara - A tameness criterion, in Volume à la mémoire d'O. Hyodo, université de Tokyo, 1993, p. 27-36.

[38] B. Mazur - Modular curves and the Eisenstein ideal, Publ. Math. I.H.É.S. 47 (1977), p. 33-186. | DOI | EuDML | Numdam | MR | Zbl

[39] K. A. Ribet - Galois representations attached to eigenforms with Nebentypus, in Modular functions of one variable, V (Proc. Second Internat. Conf, Univ. Bonn, Bonn, 1976), Springer, 1977, p. 17-51. Lecture Notes in Math., Vol. 601. | MR | Zbl

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

[41] W. H. Schikhof - Non-Archimedean calculus, Lecture notes, vol. 7812, Katholieke Universiteit Mathematisch Instituut, 1978. | MR | Zbl

[42] W. H. Schikhof - Ultrametric calculus, Cambridge Studies in Advanced Math., vol. 4, Cambridge Univ. Press, 1984. | MR | Zbl

[43] P. Schneider & J. Teitelbaum - Banach space representations and Iwasawa theory, Israel J. Math. 127 (2002), p. 359-380. | DOI | MR | Zbl

[44] P. Schneider & J. Teitelbaum - Locally analytic distributions and $p$ -adic representation theory, with applications to $G L_{2}$ , J. Amer. Math. Soc. 15 (2002), p. 443-468. | DOI | MR | Zbl

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

[46] J-P. Serre - Quelques applications du théorème de Cebotarev, Publ. Math. I.H.É.S. (1981), p. 123-201. | DOI | EuDML | Numdam | Zbl

[47] M. Vishik - Nonarchimedean measures connected with Dirichlet series, Math. USSR Sb. 28 (1976), p. 216-228. | DOI | Zbl