no. 1
Overconvergent modular forms
[Formes modulaires surconvergentes]
Pilloni, Vincent1
1Unité 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

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.

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.

DOI : 10.5802/aif.2759
Classification : 11F33
Keywords: formes modulaires $p$-adiques, formes modulaires suronvergentes, courbes modulaires
Mots-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) 
Pilloni, Vincent. Overconvergent modular forms. Annales de l'Institut Fourier, Tome 63 (2013) no. 1, pp. 219-239. doi: 10.5802/aif.2759
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