Overconvergent modular forms  [ Formes modulaires surconvergentes ]
Annales de l'Institut Fourier, Tome 63 (2013) no. 1, p. 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 : https://doi.org/10.5802/aif.2759
Classification:  11F33
Mots 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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {63},
     number = {1},
     year = {2013},
     pages = {219-239},
     doi = {10.5802/aif.2759},
     zbl = {06177080},
     mrnumber = {3097946},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2013__63_1_219_0}
}
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/item/AIF_2013__63_1_219_0/

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