no. 1
Overconvergent modular forms
[Formes modulaires surconvergentes]
Pilloni, Vincent1
1 Unité de Mathématiques Pures et Appliquées École Normale Supérieure de Lyon 46, allée d’Italie 69364 Lyon Cedex 07 (France)
Annales de l'Institut Fourier, Tome 63 (2013) no. 1, pp. 219-239.

Nous donnons une définition géométrique des formes surconvergentes de poids p-adique quelconque. Ceci nous permet d’obtenir la théorie des familles p-adiques de formes modulaires de Coleman et de reconstruire la courbe de Hecke de Coleman et Mazur sans utiliser la famille d’Eisenstein.

We give a geometric definition of overconvergent modular forms of any p-adic weight. As an application, we reprove Coleman’s theory of p-adic families of modular forms and reconstruct the eigencurve of Coleman and Mazur without using the Eisenstein family.

DOI : 10.5802/aif.2759
Classification : 11F33
Keywords: formes modulaires $p$-adiques, formes modulaires suronvergentes, courbes modulaires
Mot clés : $p$-adic modular forms, overconvergent modular forms, modular curves

Pilloni, Vincent 1

1 Unité de Mathématiques Pures et Appliquées École Normale Supérieure de Lyon 46, allée d’Italie 69364 Lyon Cedex 07 (France) 
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Pilloni, Vincent. Overconvergent modular forms. Annales de l'Institut Fourier, Tome 63 (2013) no. 1, pp. 219-239. doi : 10.5802/aif.2759. https://aif.centre-mersenne.org/articles/10.5802/aif.2759/

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