Tamely ramified Hida theory

Goldberger, Assaf; Shalit, Ehud de

doi:10.5802/aif.1875

Tamely ramified Hida theory
[Théorie de Hida modérément ramifiée]

Goldberger, Assaf ¹ ; Shalit, Ehud de ²

¹ University of Massachussetts, Department of Mathematics, Amherst MA (USA)
² Hebrew University, Institute of Mathematics, Giv'at-Ram 91904 Jerusalem (Israël)

Annales de l'Institut Fourier, Tome 52 (2002) no. 1, pp. 1-45.

Résumé
Abstract

Soit $J_{1}$ la variété jacobienne de la courbe modulaire associée à $Γ_{1} (N p), (N, p) = 1$ et soit $J_{0}$ l’autre variété associée à $Γ_{1} (N) \cap Γ_{0} (p)$ . 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 $Γ_{1} (N p), (p, N) = 1$ and $J_{0}$ the one associated with $Γ_{1} (N) \cap Γ_{0} (p)$ . 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.

MR Zbl

DOI : 10.5802/aif.1875

Classification : 11F85
Keywords: modular curve, $p$-adic periods, Hecke operators
Mot clés : courbe modulaire, périodes $p$-adiques, opérateurs de Hecke

Affiliations des auteurs :

Goldberger, Assaf ¹ ; Shalit, Ehud de ²

¹ University of Massachussetts, Department of Mathematics, Amherst MA (USA)
² Hebrew University, Institute of Mathematics, Giv'at-Ram 91904 Jerusalem (Israël)

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     title = {Tamely ramified {Hida} theory},
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     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {52},
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     doi = {10.5802/aif.1875},
     mrnumber = {1881569},
     zbl = {1048.11043},
     language = {en},
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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/articles/10.5802/aif.1875/

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