P-Adic families of Siegel modular cuspforms

2012/12/16 by Fabrizio Andreatta, Andreatta, Fabrizio, Adrain Iovita +3 · 3 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.1212.3812

arxiv created 2012/12/16 · openalex publication_date 2012/12/16 · arxiv updated 2012/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p be an odd prime and g an integer greater or equal to 2. 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 result relies on the construction of a family of sheaves of locally analytic overconvergent modular forms.

Cited by

• Modularity theorems for abelian surfaces
• Wall-crossing and p-adic Artin formalism for \rm GSp₄ × \rm GL₂ × \rm GL₂
• Certain Siegel Cusp Forms with Level are Determined by their Fundamental Fourier Coefficients

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• p-adic rigidity of eigenforms of infinite slope
• Traces on Hecke algebras and families of p-adic modular forms
• Slopes of overconvergent 2-adic modular forms
• On certain constructions of p-adic families of Siegel modular forms of even genus