Families of coherent PEL automorphic forms

TL;DR

This paper constructs Eigenvarieties for PEL Shimura varieties to interpolate automorphic forms, extending results on the Bloch-Kato conjecture for Hecke characters of quadratic imaginary fields.

Contribution

It introduces a new construction of Eigenvarieties for PEL Shimura varieties that works even with an empty ordinary locus, broadening the scope of automorphic form interpolation.

Findings

Constructed Eigenvarieties for PEL Shimura varieties with unramified primes.

Interpolated cuspidal, finite slope automorphic forms as global sections.

Extended the Bloch-Kato conjecture results for Hecke characters.

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.