Families of coherent PEL automorphic forms

Abstract

In this article we give a construction of eigenvarieties by geometrically interpolating coherent automorphic sheaves of (PEL) Shimura varieties and their global sections. The new feature is that we particularly study the case of an empty ordinary locus, and thus use a replacement of the canonical subgroup in this situation. We specifically take into account the case of small primes and use this particular construction at a specific endoscopic point to prove new cases of the Bloch-Kato conjecture for characters of an imaginary quadratic field.