$p$-adic families of Siegel modular cuspforms

Abstract

Let $p$ be an odd prime and $g\geq 2$ an integer. We prove that a finite slope Siegel cuspidal eigenform of genus $g$ can be $p$-adically deformed over the $g$-dimensional weight space. The proof of this theorem relies on the construction of a family of sheaves of locally analytic overconvergent modular forms.

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Authors

Fabrizio Andreatta

Università Statale di Milano, Milano, Italy

Adrian Iovita

Concordia University, Montreal, Quebec, Canada, Universtità Degli Studi di Padova, Padova, Italy

Vincent Pilloni

Chargé de recherche en mathématiques au CNRS, Ecole normale supérieure de Lyon, Lyon, France