@incollection{AST_2011__339__31_0, 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}, note = {talk:1013}, 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/} }
TY - CHAP AU - Emerton, Matthew TI - $p$-adic families of modular forms [after Hida, Coleman, and Mazur] BT - Séminaire Bourbaki, volume 2009/2010, exposés 1012-1026 AU - Collectif T3 - Astérisque N1 - talk:1013 PY - 2011 SP - 31 EP - 61 IS - 339 PB - Société mathématique de France UR - http://archive.numdam.org/item/AST_2011__339__31_0/ LA - en ID - AST_2011__339__31_0 ER -
%0 Book Section %A Emerton, Matthew %T $p$-adic families of modular forms [after Hida, Coleman, and Mazur] %B Séminaire Bourbaki, volume 2009/2010, exposés 1012-1026 %A Collectif %S Astérisque %Z talk:1013 %D 2011 %P 31-61 %N 339 %I Société mathématique de France %U http://archive.numdam.org/item/AST_2011__339__31_0/ %G en %F AST_2011__339__31_0
Emerton, Matthew. $p$-adic families of modular forms [after Hida, Coleman, and Mazur], in Séminaire Bourbaki, volume 2009/2010, exposés 1012-1026, Astérisque, no. 339 (2011), Talk no. 1013, 31 p. http://archive.numdam.org/item/AST_2011__339__31_0/
[1] -adic deformations of cohomology on : the non-ordinary case", preprint, 2000.
& - "[2] Hecke operators on ", Math. Ann. 185 (1970), p. 134-160. | DOI | EuDML | MR | Zbl
& - "[3] On the density of modular points in universal deformation spaces", Amer. J. Math. 123 (2001), p. 985-1007. | DOI | MR | Zbl
- "[4] Eigenvarieties", in -functions and Galois representations, London Math. Soc. Lecture Note Ser., vol. 320, Cambridge Univ. Press, 2007, p. 59-120. | DOI | MR | Zbl
- "[5] Companion forms and weight one forms", Ann. of Math. 149 (1999), p. 905-919. | DOI | EuDML | MR | Zbl
& - "[6] On some results of Atkin and Lehner", Math. Ann. 201 (1973), p. 301-314. | DOI | EuDML | MR | Zbl
- "[7] Classical and overconvergent modular forms", Invent. Math. 124 (1996), p. 215-241. | DOI | MR | Zbl
- "[8] Classical and overconvergent modular forms of higher level", J. Théor. Nombres Bordeaux 9 (1997), p. 395-403. | DOI | EuDML | Numdam | MR | Zbl
, "[9] On the semi-simplicity of the -operator on modular forms", Math. Ann. 310 (1998), p. 119-127. | DOI | MR | Zbl
& - "[10] 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] Formes modulaires et représentations -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] Formes modulaires de poids ", Ann. Sci. École Norm. Sup. 7 (1974), p. 507-530. | DOI | EuDML | Numdam | MR | Zbl
& - "[13] Quaternäre quadratische Formen und die Riemannsche Vermutung für die Kongruenzzetafunktion", Arch. Math. 5 (1954), p. 355-366. | DOI | MR | Zbl
- "[14] Jacquet modules of locally analytic representations of -adic reductive groups. I. Construction and first properties", Ann. Sci. École Norm. Sup. 39 (2006), p. 775-839. | DOI | EuDML | MR | Zbl
- "[15] On the Interpolation of Systems of eigenvalues attached to automorphic Hecke eigenforms", Invent. Math. 164 (2006), p. 1-84. | DOI | MR | Zbl
, "[16] Local-global compatibility in the -adic Langlands programme for ", preprint, 2010.
, "[17] Le corps des périodes -adiques", Astérisque 223 (1994), p. 59-111. | Numdam | MR | Zbl
- "[18] 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] Arithmetic of -adic modular forms, Lecture Notes in Math., vol. 1304, Springer, 1988. | MR | Zbl
-[20] Deforming Galois representations: controlling the conductor", J. Number Theory 34 (1990), p. 95-113. | DOI | MR | Zbl
, "[21] 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] Galois representations into attached to ordinary cusp forms", Invent. Math. 85 (1986), p. 545-613. | DOI | EuDML | MR | Zbl
- "[23] Iwasawa modules attached to congruences of cusp forms", Ann. Sci. École Norm. Sup. 19 (1986), p. 231-273. | DOI | EuDML | Numdam | MR | Zbl
, "[24] Kroneckerian model of fields of elliptic modular functions", Amer. J. Math. 81 (1959), p. 561-577. | DOI | MR | Zbl
- "[25] Automorphic forms on , Lecture Notes in Math., vol. 114, Springer, 1970. | MR | Zbl
& -[26] Congruences between systems of eigenvalues of modular forms", Trans. Amer. Math. Soc. 270 (1982), p. 269-285. | DOI | MR | Zbl
- "[27] -adic interpolation of real analytic Eisenstein series", Ann. of Math. 104 (1976), p. 459-571. | DOI | MR | Zbl
- "[28] Overconvergent modular forms and the Fontaine-Mazur conjecture", Invent. Math. 153 (2003), p. 373-454. | DOI | MR | Zbl
- "[29] Geometric deformations of modular Galois representations", Invent. Math. 157 (2004), p. 275-328. | DOI | MR | Zbl
, "[30] The Fontaine-Mazur conjecture for ", J. Amer. Math. Soc. 22 (2009), p. 641-690. | DOI | MR | Zbl
, "[31] Deforming Galois representations", in Galois groups over (Berkeley, CA, 1987), Math. Sci. Res. Inst. Publ., vol. 16, Springer, 1989, p. 385-437. | DOI | MR | Zbl
-"[32] An "infinite fern" in the Universal deformation space of Galois representations", Collect. Math. 48 (1997), p. 155-193. | EuDML | MR | Zbl
, "[33] 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] On -adic analytic families of Galois representations", Compositio Math. 59 (1986), p. 231-264. | EuDML | Numdam | MR | Zbl
& - "[35] 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] Modular forms and -adic Hodge theory", Invent. Math. 129 (1997), p. 607-620. | DOI | MR | Zbl
- "[37] Formes modulaires et fonctions zêta -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] Correspondances modulaires et les fonctions de courbes algébriques", J. Math. Soc. Japan 10 (1958), p. 1-28. | DOI | MR | Zbl
- "[39] 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] Residually reducible representations and modular forms", Publ. Math. I.H.É.S. 89 (1999), p. 5-126. | EuDML | MR | Zbl
& - "[41] Nearly ordinary deformations of irreducible residual representations", Ann. Fac. Sci. Toulouse Math. 10 (2001), p. 185-215. | DOI | EuDML | Numdam | MR | Zbl
& , "[42] Rigid analytic modular symbols", preprint, 1994.
- "[43] Ring-theoretic properties of certain hecke algebras", Ann. of Math. 141 (1995), p. 553-572. | DOI | MR | Zbl
& - "[44] On ordinary -adic representations associated to modular forms", Invent. Math. 94 (1988), p. 529-573. | DOI | EuDML | MR | Zbl
- "[45] Modular elliptic curves and Fermat's last theorem", Ann. of Math. 141 (1995), p. 443-551. | DOI | MR | Zbl
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