Ramification of Hilbert eigenvarieties at classical points

2019/05/14 by Chi-Yun Hsu, Hsu, Chi-Yun
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1905.05687

openalex publication_date 2019/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Andreatta-Iovita-Pilloni constructed eigenvarieties for cuspidal Hilbert modular forms. The eigenvariety has a natural map to the weight space, called the weight map. At a classical point, we compute a lower bound of the dimension of the tangent space of the fiber of the weight map using Galois deformation theory. Along with the classicality theorem due to Tian-Xiao, this enables us to characterize the classical points of the eigenvariety which are ramified over the weight space, in terms of the local splitting behavior of the associated Galois representation.

Citations

• p-adic Cohomology and classicality of overconvergent Hilbert modular forms
• On ordinary ?-adic representations associated to modular forms
• Caractérisation des caractères et Pseudo-caractères

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