A p-adic family of dihedral (phi,Gamma)-modules

2009/03/12 by Laurent Berger, Berger, Laurent
Mathematics · #11F33 #11F80 #11S20 #11S31 #12H25 #14D15 #14F30 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F33 #msc:11F80 #msc:11S20 #msc:11S31 #msc:12H25 #msc:14D15 #msc:14F30

paper · pdf · doi:10.48550/arxiv.0903.2183

10 pages

arxiv created 2009/03/12 · openalex publication_date 2009/03/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The goal of this article is to construct explicitly a p-adic family of representations (which are dihedral representations), to construct their associated (phi,Gamma)-modules by writing down explicit matrices for phi and for the action of Gamma, and finally to determine which of these are trianguline.

Related

• Families of p-adic Galois representations and (phi,Gamma)-modules
• Families of trianguline representations and finite slope spaces
• Arithmetic families of (φ, Γ)-modules and locally analytic representations of GL₂(Q_p)
• Some questions about representations of p-adic groups
• Construction of some families of 2-dimensional crystalline representations