Le halo spectral

Andreatta, Fabrizio; Iovita, Adrian; Pilloni, Vincent

doi:10.24033/asens.2362

Le halo spectral
[The spectral halo]

Andreatta, Fabrizio ; Iovita, Adrian ; Pilloni, Vincent

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 51 (2018) no. 3, pp. 603-655.

Résumé
Abstract

We construct a space of overconvergent modular forms of characteristic $p$ , a compact operator on this space and we show that the characteristic series of this operator is the reduction modulo $p$ of Coleman's universal series. We prove that finite slope overconvergent modular forms in positive characteristic can be deformed to characteristic 0.

Nous construisons un espace de formes surconvergentes en caractéristique $p$ , un opérateur compact sur cet espace et nous montrons que la série caractéristique de cet opérateur est la réduction modulo $p$ de la série universelle de Coleman. Nous démontrons que les formes surconvergentes en caractéristique $p$ de pente finie se déforment vers la caractéristique 0.

MR Zbl

DOI : 10.24033/asens.2362

Classification : 11F33, 11G18, 14G35.
Keywords: Formes modulaires, formes modulaires $p$-adiques.
Mot clés : Modular forms, $p$-adic modular forms.

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     title = {Le halo spectral},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {603--655},
     publisher = {Soci\'et\'e Math\'ematique de France. Tous droits r\'eserv\'es},
     volume = {Ser. 4, 51},
     number = {3},
     year = {2018},
     doi = {10.24033/asens.2362},
     mrnumber = {3831033},
     zbl = {1444.11075},
     language = {en},
     url = {http://archive.numdam.org/articles/10.24033/asens.2362/}
}

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Andreatta, Fabrizio; Iovita, Adrian; Pilloni, Vincent. Le halo spectral. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 51 (2018) no. 3, pp. 603-655. doi : 10.24033/asens.2362. http://archive.numdam.org/articles/10.24033/asens.2362/

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