Dihedral Iwasawa theory of nearly ordinary quaternionic automorphic forms

Abstract

AbstractLetπ(f) be a nearly ordinary automorphic representation of the multiplicative group of an indefinite quaternion algebraBover a totally real fieldFwith associated Galois representationρf. LetKbe a totally complex quadratic extension ofFembedding inB. Using families of CM points on towers of Shimura curves attached toBandK, we construct an Euler system forρf. We prove that it extends top-adic families of Galois representations coming from Hida theory and dihedral ℤdp-extensions. When this Euler system is non-trivial, we prove divisibilities of characteristic ideals for the main conjecture in dihedral and modular Iwasawa theory.