[Formes modulaires surconvergentes]
Nous donnons une définition géométrique des formes surconvergentes de poids -adique quelconque. Ceci nous permet d’obtenir la théorie des familles -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 -adic weight. As an application, we reprove Coleman’s theory of -adic families of modular forms and reconstruct the eigencurve of Coleman and Mazur without using the Eisenstein family.
Keywords: formes modulaires $p$-adiques, formes modulaires suronvergentes, courbes modulaires
Mot clés : $p$-adic modular forms, overconvergent modular forms, modular curves
@article{AIF_2013__63_1_219_0,
author = {Pilloni, Vincent},
title = {Overconvergent modular forms},
journal = {Annales de l'Institut Fourier},
pages = {219--239},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {63},
number = {1},
year = {2013},
doi = {10.5802/aif.2759},
zbl = {06177080},
mrnumber = {3097946},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.2759/}
}
TY - JOUR AU - Pilloni, Vincent TI - Overconvergent modular forms JO - Annales de l'Institut Fourier PY - 2013 SP - 219 EP - 239 VL - 63 IS - 1 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2759/ DO - 10.5802/aif.2759 LA - en ID - AIF_2013__63_1_219_0 ER -
Pilloni, Vincent. Overconvergent modular forms. Annales de l'Institut Fourier, Tome 63 (2013) no. 1, pp. 219-239. doi : 10.5802/aif.2759. http://www.numdam.org/articles/10.5802/aif.2759/
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