Families of coherent PEL automorphic forms

2019/09/13 by Valentín Hernández, Hernandez, Valentin
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1909.06127

openalex publication_date 2019/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct Eigenvarieties for PEL Shimura varieties which interpolate cuspidal, finite slope automorphic forms for PEL Shimura varieties appearing as global sections of (coherent) automorphic sheaves, under the hypothesis that the primes are unramified in the Shimura datum, but allowing the ordinary locus to be empty. We then use this construction to extend previous results on the Bloch-Kato conjecture for Hecke characters of a quadratic imaginary field.

Related

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• Computing automorphic forms on Shimura curves over fields with arbitrary class number
• The trace formula and the existence of PEL type Abelian varieties modulo p
• Griffiths-Schmid conditions for automorphic forms via characteristic p