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Dihedral Iwasawa theory of nearly ordinary quaternionic automorphic forms

Published online by Cambridge University Press:  13 December 2012

Olivier Fouquet
Affiliation:
Département de Mathématiques, Faculté des Sciences d’Orsay, Université Paris-Sud 11, F-91405 Orsay Cedex, Bâtiment 425, France (email: olivier.fouquet@polytechnique.org)
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Abstract

Let π(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 ρf. 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 ρf. We prove that it extends to p-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.

Type
Research Article
Copyright
Copyright © 2012 The Author(s)

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