Quaternionic modular forms of any weight

2012/06/25 by Riccardo Brasca, Brasca, Riccardo · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.1206.5675

18 pages. Preliminary version

arxiv created 2012/06/25 · arxiv updated 2012/06/26

Abstract

In this work we construct an eigencurve for p-adic modular forms attached to an indefinite quaternion algebra over Q. Our theory includes the definition, both as rules on test objects and sections of line bundle, of p-adic modular forms, convergent and overconvergent, of any p-adic weight. We prove that our modular forms can be put in analytic families over the weight space and we introduce the Hecke operators U and T_l, that can also be put in families. We show that the U-operator acts compactly on the space of overconvergent modular forms. We finally construct the eigencurve, a rigid analytic variety whose points correspond to systems of overconvergent eigenforms of finite slope with respect to the U-operator.

Cited by

• On quaternionic ordinary families of modular forms and p-adic L-functions

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