Dihedral Iwasawa theory of nearly ordinary quaternionic automorphic forms

作者：Fouquet Olivier^*

来源：Compositio Mathematica, 2013, 149(3): 356-416.

DOI：10.1112/S0010437X12000619

• p-adic families of automorphic forms
• Iwasawa main conjecture
• Euler systems

Let pi(f) be a nearly ordinary automorphic representation of the multiplicative group of an indefinite quaternion algebra B over a totally real field F with associated Galois representation rho(f). Let K be a totally complex quadratic extension of F embedding in B. Using families of CM points on towers of Shimura curves attached to B and K, we construct an Euler system for rho(f). We prove that it extends to p-adic families of Galois representations coming from Hida theory and dihedral Z(p)(d)-extensions. When this Euler system is non-trivial, we prove divisibilities of characteristic ideals for the main conjecture in dihedral and modular Iwasawa theory.

• 出版日期2013-3