Deformations of trianguline B-pairs and Zariski density of two dimensional crystalline representations

2010/06/25 by Kentaro Nakamura, Nakamura, Kentaro · 4 citations
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #11F80 (primary) #11F85 #11S25 (secondary) #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1006.4891

openalex publication_date 2010/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this article is to study deformation theory of trianguline B-pairs for any p-adic field. For benign B-pairs, a special good class of trianguline B-pairs, we prove a main theorem concerning tangent spaces of these deformation spaces. These are generalizations of Bellaiche-Chenevier's and Chenevier's works in the Q_p case, where they used (ϕ,Γ)-modules over the Robba ring instead of using B-pairs. As an application of this theory, in the final chapter, we prove a theorem concerning Zariski density of two dimensional crystalline representations for any p-adic field, which is a generalization of Colmez and Kisin's results in the Q_p case.

Citations

• Zariski density of crystalline representations for any p-adic field

Cited by

• Change of weights operations for triangulated (φ,Γ)-modules
• Partial Bloch--Kato Selmer groups of B-pairs as delta functors
• Iwasawa theory of de Rham (ϕ,Γ)-modules over the Robba rings
• Cohomology of arithmetic families of (phi,Gamma)-modules

Related

• Deformations of trianguline B-pairs
• Zariski density of crystalline representations for any p-adic field
• Zariski density of crystalline points on \GSp_2n-valued local deformation rings
• Sur la densité des représentations cristallines du groupe de Galois absolu de Q_p
• On triangulable tensor products of B-pairs and trianguline\n representations