$p$-adic families of modular forms [after Hida, Coleman, and Mazur]

p

-adic families of modular forms [after Hida, Coleman, and Mazur]

Emerton, Matthew

Séminaire Bourbaki, volume 2009/2010, exposés 1012-1026, Astérisque, no. 339 (2011), Exposé no. 1013, 31 p.

MR Zbl | 2 citations dans Numdam

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     author = {Emerton, Matthew},
     title = {$p$-adic families of modular forms [after {Hida,} {Coleman,} and {Mazur]}},
     booktitle = {S\'eminaire Bourbaki, volume 2009/2010, expos\'es 1012-1026},
     series = {Ast\'erisque},
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     pages = {31--61},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {339},
     year = {2011},
     mrnumber = {2906349},
     zbl = {1356.11026},
     language = {en},
     url = {http://archive.numdam.org/item/AST_2011__339__31_0/}
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Emerton, Matthew. $p$-adic families of modular forms [after Hida, Coleman, and Mazur], dans Séminaire Bourbaki, volume 2009/2010, exposés 1012-1026, Astérisque, no. 339 (2011), Exposé no. 1013, 31 p. http://archive.numdam.org/item/AST_2011__339__31_0/

Bibliographie
Cité par

[1] A. Ash & G. Stevens - " $p$ -adic deformations of cohomology on $G L (n)$ : the non-ordinary case", preprint, 2000.

[2] A. O. L. Atkin & J. Lehner - "Hecke operators on $Γ_{0} (m)$ ", Math. Ann. 185 (1970), p. 134-160. | DOI | EuDML | MR | Zbl

[3] G. Böckle - "On the density of modular points in universal deformation spaces", Amer. J. Math. 123 (2001), p. 985-1007. | DOI | MR | Zbl

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

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

[6] W. Casselman - "On some results of Atkin and Lehner", Math. Ann. 201 (1973), p. 301-314. | DOI | EuDML | MR | Zbl

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

[8] 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

[9] R. F. Coleman & B. Edixhoven - "On the semi-simplicity of the $U_{p}$ -operator on modular forms", Math. Ann. 310 (1998), p. 119-127. | DOI | MR | Zbl

[10] 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

[11] P. Deligne - "Formes modulaires et représentations $ℓ$ -adiques", Séminaire Bourbaki, volume 1968/1969, exposé n° 355, Lecture Notes in Math., vol. 179, 1971, p. 139-172. | DOI | EuDML | Numdam | MR | Zbl

[12] P. Deligne & J-P. Serre - "Formes modulaires de poids $1$ ", Ann. Sci. École Norm. Sup. 7 (1974), p. 507-530. | DOI | EuDML | Numdam | MR | Zbl

[13] M. Eichler - "Quaternäre quadratische Formen und die Riemannsche Vermutung für die Kongruenzzetafunktion", Arch. Math. 5 (1954), p. 355-366. | DOI | MR | Zbl

[14] 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 | MR | Zbl

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

[16] M. Emerton, "Local-global compatibility in the $p$ -adic Langlands programme for $G L_{2} (ℚ_{p})$ ", preprint, 2010.

[17] J.-M. Fontaine - "Le corps des périodes $p$ -adiques", Astérisque 223 (1994), p. 59-111. | Numdam | MR | Zbl

[18] J.-M. Fontaine & B. Mazur - "Geometric Galois representations", in Elliptic curves, modular forms, & Fermat's last theorem (Hong Kong, 1993), Ser. Number Theory, I, Int. Press, Cambridge, MA, 1995, p. 41-78. | MR | Zbl

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

[20] F. Q. Gouvêa, "Deforming Galois representations: controlling the conductor", J. Number Theory 34 (1990), p. 95-113. | DOI | MR | Zbl

[21] F. Q. Gouvêa & B. Mazur - "On the density of modular representations", in Computational perspectives on number theory (Chicago, IL, 1995), AMS/IP Stud. Adv. Math., vol. 7, Amer. Math. Soc., 1998, p. 127-142. | DOI | MR | Zbl

[22] 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

[23] H. Hida, "Iwasawa modules attached to congruences of cusp forms", Ann. Sci. École Norm. Sup. 19 (1986), p. 231-273. | DOI | EuDML | Numdam | MR | Zbl

[24] J.-I. Igusa - "Kroneckerian model of fields of elliptic modular functions", Amer. J. Math. 81 (1959), p. 561-577. | DOI | MR | Zbl

[25] H. Jacquet & R. P. Langlands - Automorphic forms on $G L (2)$ , Lecture Notes in Math., vol. 114, Springer, 1970. | MR | Zbl

[26] N. Jochnowitz - "Congruences between systems of eigenvalues of modular forms", Trans. Amer. Math. Soc. 270 (1982), p. 269-285. | DOI | MR | Zbl

[27] N. M. Katz - " $p$ -adic interpolation of real analytic Eisenstein series", Ann. of Math. 104 (1976), p. 459-571. | DOI | MR | Zbl

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

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

[30] M. Kisin, "The Fontaine-Mazur conjecture for $G L_{2}$ ", J. Amer. Math. Soc. 22 (2009), p. 641-690. | DOI | MR | Zbl

[31] B. Mazur -"Deforming Galois representations", in Galois groups over $𝐐$ (Berkeley, CA, 1987), Math. Sci. Res. Inst. Publ., vol. 16, Springer, 1989, p. 385-437. | DOI | MR | Zbl

[32] B. Mazur, "An "infinite fern" in the Universal deformation space of Galois representations", Collect. Math. 48 (1997), p. 155-193. | EuDML | MR | Zbl

[33] B. Mazur & J. Tilouine - "Représentations galoisiennes, différentielles de Kähler et "conjectures principales"", Publ. Math. I.H.É.S. 71 (1990), p. 65-103. | DOI | EuDML | Numdam | MR | Zbl

[34] B. Mazur & A. J. Wiles - "On $p$ -adic analytic families of Galois representations", Compositio Math. 59 (1986), p. 231-264. | EuDML | Numdam | MR | Zbl

[35] 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), Lecture Notes in Math., Vol. 601, Springer, 1977, p. 17-51. | MR | Zbl

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

[37] J-P. Serre - "Formes modulaires et fonctions zêta $p$ -adiques", in Modular functions of one variable, III (Proc. Internat. Summer School, Univ. Antwerp, 1972), Lecture Notes in Math., vol. 350, Springer, 1973, p. 191-268. | DOI | MR | Zbl

[38] G. Shimura - "Correspondances modulaires et les fonctions $ζ$ de courbes algébriques", J. Math. Soc. Japan 10 (1958), p. 1-28. | DOI | MR | Zbl

[39] G. Shimura, Introduction to the arithmetic theory of automorphic functions, Publications of the Mathematical Society of Japan, No. 11. Iwanami Shoten, Publishers, Tokyo, 1971. | MR | Zbl

[40] C. M. Skinner & A. J. Wiles - "Residually reducible representations and modular forms", Publ. Math. I.H.É.S. 89 (1999), p. 5-126. | EuDML | MR | Zbl

[41] C. M. Skinner & A. J. Wiles, "Nearly ordinary deformations of irreducible residual representations", Ann. Fac. Sci. Toulouse Math. 10 (2001), p. 185-215. | DOI | EuDML | Numdam | MR | Zbl

[42] G. Stevens - "Rigid analytic modular symbols", preprint, 1994.

[43] R. Taylor & A. J. Wiles - "Ring-theoretic properties of certain hecke algebras", Ann. of Math. 141 (1995), p. 553-572. | DOI | MR | Zbl

[44] A. J. Wiles - "On ordinary $λ$ -adic representations associated to modular forms", Invent. Math. 94 (1988), p. 529-573. | DOI | EuDML | MR | Zbl

[45] A. J. Wiles, "Modular elliptic curves and Fermat's last theorem", Ann. of Math. 141 (1995), p. 443-551. | DOI | MR | Zbl