Families of trianguline representations and finite slope spaces

2012/02/20 by Eugen Hellmann, Hellmann, Eugen
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.1202.4408

arxiv created 2012/02/20 · openalex publication_date 2012/02/20 · arxiv updated 2012/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We apply the theory of families of (phi,Gamma)-modules to trianguline families as defined by Chenevier. This yields a new definition of Kisin's finite slope subspace as well as higher dimensional analogues. Especially we show that these finite slope spaces contain eigenvarieties for unitary groups as closed subspaces. This implies that the representations arising from overconvergent p-adic automorphic forms on certain unitary groups are trianguline when restricted to the local Galois group.

Related

• Modularity of trianguline Galois representations
• Universal eigenvarieties, trianguline Galois representations, and p-adic Langlands functoriality
• Sur la densité des représentations cristallines du groupe de Galois absolu de Q_p
• p-adic rigidity of eigenforms of infinite slope
• A p-adic family of dihedral (phi,Gamma)-modules