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Dihedral Iwasawa theory of nearly ordinary quaternionic automorphic forms

Part of: Algebraic number theory: global fields Arithmetic algebraic geometry Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  13 December 2012

Olivier Fouquet
Olivier Fouquet*
Affiliation:
Département de Mathématiques, Faculté des Sciences d’Orsay, Université Paris-Sud 11, F-91405 Orsay Cedex, Bâtiment 425, France (email: [email protected])
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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.

Keywords

p-adic families of automorphic formsIwasawa main conjectureEuler systems

MSC classification

Secondary: 11F33: Congruences for modular and $p$-adic modular forms 11F80: Galois representations 11G18: Arithmetic aspects of modular and Shimura varieties 11G40: $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture 11R23: Iwasawa theory 11R34: Galois cohomology
Type
Research Article
Information
Compositio Mathematica , Volume 149 , Issue 3 , March 2013 , pp. 356 - 416
Copyright
Copyright © 2012 The Author(s)

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