Familles de formes modulaires de Drinfeld pour le groupe général linéaire

Nicole, Marc-Hubert; Rosso, Giovanni

doi:10.1090/tran/8314

Familles de formes modulaires de Drinfeld pour le groupe général linéaire
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by Marc-Hubert Nicole and Giovanni Rosso PDF

Trans. Amer. Math. Soc. 374 (2021), 4227-4266

Abstract:

Soient $F$ un corps de fonctions sur $\mathbb {F}_q$, $A$ l’anneau des fonctions régulières hors d’une place $\infty$ et $\mathfrak {p}$ un idéal premier de $A$. En premier lieu, nous développons la théorie de Hida pour les formes modulaires de Drinfeld de rang $r$ qui sont de pente nulle pour l’opérateur de Hecke $\mathrm {U}_{\pi }$ convenablement défini. En second lieu, nous montrons en pente finie l’existence de familles de formes modulaires de Drinfeld variant continûment selon le poids. En troisième lieu, nous prouvons un résultat de classicité: une forme modulaire de Drinfeld surconvergente de pente suffisamment petite par rapport au poids est une forme modulaire de Drinfeld classique.

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