p-adic families of modular forms for Hodge type Shimura varieties with non-empty ordinary locus

2020/09/15 by Riccardo Brasca, Brasca, Riccardo
Mathematics · #11F33 (Primary) #11F55 (Secondary) #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2009.07150

openalex publication_date 2020/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalize some of the results of Andreatta, Iovita, and Pilloni and the author to Hodge type Shimura varieties having non-empty ordinary locus. For any p-adic weight κ, we give a geometric definition of the space of overconvergent modular forms of weight κ in terms of sections of a sheaf. We show that our sheaves live in analytic families, interpolating the classical sheaves for integral weights. We define an action of the Hecke algebra, including a completely continuous operator at p. In some simple cases, we also build the eigenvariety.

Citations

• Eigenvarieties for non-cuspidal modular forms over certain PEL Shimura varieties

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