Tamely ramified Hida theory  [ Théorie de Hida modérément ramifiée ]
Annales de l'Institut Fourier, Tome 52 (2002) no. 1, p. 1-45
Soit J 1 la variété jacobienne de la courbe modulaire associée à Γ 1 (Np),(N,p)=1 et soit J 0 l’autre variété associée à Γ 1 (N)Γ 0 (p). Nous étudions J 1 [p-1] comme un module de Hecke et de Galois. On trouve une relation entre une matrice de périodes p-adiques et la variation infinitésimale de l’opérateur U p .
Let J 1 be the Jacobian of the modular curve associated with Γ 1 (Np),(p,N)=1 and J 0 the one associated with Γ 1 (N)Γ 0 (p). We study J 1 [p-1] as a Hecke and Galois-module. We relate a certain matrix of p-adic periods to the infinitesimal deformation of the U p -operator.
DOI : https://doi.org/10.5802/aif.1875
Classification:  11F85
Mots clés: courbe modulaire, périodes p-adiques, opérateurs de Hecke
@article{AIF_2002__52_1_1_0,
     author = {Goldberger, Assaf and Shalit, Ehud de},
     title = {Tamely ramified Hida theory},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {52},
     number = {1},
     year = {2002},
     pages = {1-45},
     doi = {10.5802/aif.1875},
     zbl = {1048.11043},
     mrnumber = {1881569},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2002__52_1_1_0}
}
Goldberger, Assaf; Shalit, Ehud de. Tamely ramified Hida theory. Annales de l'Institut Fourier, Tome 52 (2002) no. 1, pp. 1-45. doi : 10.5802/aif.1875. http://www.numdam.org/item/AIF_2002__52_1_1_0/

[ALe] A.O.L. Atkin; J. Lehner Hecke operators on Γ 0 (m), Math. Annalen, Tome 185 (1970), pp. 134-160 | Article | MR 268123 | Zbl 0177.34901

[ALi] A.O.L. Atkin; W. Li Twists of newforms and pseudo-eigenvalues of W-operators, Inv. Math., Tome 43 (1978), pp. 221-244 | Article | MR 508986 | Zbl 0369.10016

[B] S. Bosch Abelian varieties from the rigid-analytic viewpoint, Barsotti Symposium in Algebraic Geometry, Academic Press (1994), pp. 51-63 | Zbl 0836.14028

[BLR] S. Bosch; W. Lütkebohmert; M. Raynaud Néron models, Springer, Ergebnisse der Math., 3 folge, Tome 21 (1990) | MR 1045822 | Zbl 0705.14001

[DR] P. Deligne; M. Rapoport Schémas de modules de courbes elliptiques, Springer, LNM, Tome 349 (1973) | MR 337993 | Zbl 0281.14010

[dS1] E. De Shalit On certain Galois representations related to the modular curve X 1 (p), Compositio Math., Tome 95 (1995), pp. 69-100 | Numdam | MR 1314697 | Zbl 0853.11045

[dS2] E. De Shalit p-adic periods and modular symbols of elliptic curves of prime conductor, Inv. Math., Tome 121 (1995), pp. 225-255 | Article | MR 1346205 | Zbl 1044.11576

[dS3] E. De Shalit Néron models and p-adic uniformization of generalized Jacobians (In preparation)

[E] B. Edixhoven L'action de l'algebre de Hecke sur les groupes de composantes des jacobiennes des courbes modulaires est ``Eisenstein'', Astérisque, Tome 196-197 (1991), pp. 59-70 | MR 1141457 | Zbl 0781.14019

[GS] R. Greenberg; G. Stevens p-adic L-functions and p-adic periods of modular forms, Inv. Math., Tome 111 (1993), pp. 407-447 | Article | MR 1198816 | Zbl 0778.11034

[H] H. Hida Galois representations into GL 2 ( p [[X]]) attached to ordinary cusp forms, Inv. Math., Tome 85 (1986), pp. 545-613 | Article | MR 848685 | Zbl 0612.10021

[KM] N. Katz; B. Mazur Arithmetic moduli of elliptic curves, Princeton, Ann. Math. Studies, Tome 108 (1985) | MR 772569 | Zbl 0576.14026

[M] B. Mazur Modular curves and the Eisenstein ideal, Publ. Math. I.H.E.S, Tome 47 (1977), pp. 33-186 | Numdam | MR 488287 | Zbl 0394.14008

[MT] B. Mazur; J. Tate Refined conjectures of "Birch and Swinnerton-Dyer type", Duke Math. J., Tome 54 (1987), pp. 711-750 | MR 899413 | Zbl 0636.14004

[MTT] B. Mazur; J. Tate; J. Teitelbaum On p-adic analogues of the conjectures of Birch and Swinerton-Dyer, Inv. Math., Tome 84 (1986), pp. 1-48 | Article | MR 830037 | Zbl 0699.14028

[MW1] B. Mazur; A. Wiles Class fields of abelian extensions of Q, Inv. Math., Tome 76 (1984), pp. 179-330 | Article | MR 742853 | Zbl 0545.12005

[MW2] B. Mazur; A. Wiles On p-adic analytic families of Galois representations, Compositio Math., Tome 59 (1986), pp. 231-264 | Numdam | MR 860140 | Zbl 0654.12008

[Ri] K. Ribet Congruence relations between modular forms, Proc. International Congress of Math., Tome 17 (1983), pp. 503-514 | Zbl 0575.10024

[SGA7] A. Grothendieck Modéles de Néron et monodromie (exposé IX), SGA 71, Springer (LNM) Tome 288 (1972) | Zbl 0248.14006

[W] A. Wiles Modular elliptic curves and Fermat's last theorem, Ann. of Math., Tome 141 (1995), pp. 443-551 | Article | MR 1333035 | Zbl 0823.11029