Gauss–Manin connections for p-adic families of nearly overconvergent modular forms  [ Connexions de Gauss–Manin pour les families p-adiques de formes modulaires quasi-surconvergentes ]
Annales de l'Institut Fourier, Tome 64 (2014) no. 6, pp. 2449-2464.

Nous obtenons l’interpolation de la connexion de Gauss–Manin en familles p-adiques de formes modulaires quasi-surconvergentes. Ceci donne une famille d’opérateurs différentiels à la Maass–Shimura qui envoie l’espace de formes modulaires quasi-surconvergentes de type r dans celui de formes modulaires quasi-surconvergentes de type r+1 et de poids p-adique augmenté par 2. Notre méthode est purement géométrique, elle utlise les constructions géométriques des courbes de Hecke dues à Andreatta–Iovita–Stevens et Pilloni, et devrait donc se généraliser aux groupes de rang supérieur.

We interpolate the Gauss–Manin connection in p-adic families of nearly overconvergent modular forms. This gives a family of Maass–Shimura type differential operators from the space of nearly overconvergent modular forms of type r to the space of nearly overconvergent modular forms of type r+1 with p-adic weight shifted by 2. Our construction is purely geometric, using Andreatta–Iovita–Stevens and Pilloni’s geometric construction of eigencurves, and should thus generalize to higher rank groups.

Reçu le : 2013-09-21
Accepté le : 2014-07-09
DOI : https://doi.org/10.5802/aif.2916
Classification : 11F33,  14F40
Mots clés : Connexions de Gauss–Manin, Formes modulaires quasi-surconvergents, courbes de Hecke, Familles p-adiques de formes modulaires
@article{AIF_2014__64_6_2449_0,
     author = {Harron, Robert and Xiao, Liang},
     title = {Gauss--Manin connections for $p$-adic families of nearly overconvergent modular forms},
     journal = {Annales de l'Institut Fourier},
     pages = {2449--2464},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {64},
     number = {6},
     year = {2014},
     doi = {10.5802/aif.2916},
     zbl = {06387343},
     mrnumber = {3331170},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2014__64_6_2449_0/}
}
Harron, Robert; Xiao, Liang. Gauss–Manin connections for $p$-adic families of nearly overconvergent modular forms. Annales de l'Institut Fourier, Tome 64 (2014) no. 6, pp. 2449-2464. doi : 10.5802/aif.2916. https://aif.centre-mersenne.org/item/AIF_2014__64_6_2449_0/

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