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1 results

  • Dihedral Iwasawa theory of nearly ordinary quaternionic automorphic forms

  • Part of
  • Olivier Fouquet
  • Journal:
    Compositio Mathematica / Volume 149 / Issue 3 / March 2013
    Published online by Cambridge University Press:
    13 December 2012, pp. 356-416
    Print publication:
    March 2013
    • Article
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  • 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.