Dihedral Iwasawa theory of nearly ordinary quaternionic automorphic forms

2012/12/13 by Olivier Fouquet · 6 citations
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Algebraic structures and combinatorial models

paper · pdf · doi:10.1112/s0010437x12000619

Abstract

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 ρ 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 ρ f . We prove that it extends to p -adic families of Galois representations coming from Hida theory and dihedral ℤ d p -extensions. When this Euler system is non-trivial, we prove divisibilities of characteristic ideals for the main conjecture in dihedral and modular Iwasawa theory.

Citations

• On ordinary ?-adic representations associated to modular forms
• Good Reduction of Abelian Varieties

Cited by

• On anticyclotomic Euler and Kolyvagin systems
• Quaternionic big Heegner points over totally real fields
• Quaternionic families of Heegner points and p-adic L-functions
• Quaternion algebras, Heegner points and the arithmetic of Hida families
• Iwasawa Main Conjecture for Heegner Points: Supersingular Case
• A refined Beilinson-Bloch conjecture for motives of modular forms
• Quaternionic Kolyvagin systems and Iwasawa theory for Hida families

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