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

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.

The half of this article is almost same as the article which the author submitted in February 2010, the author adds the proof of Zariski density of crystalline representations

References in corpus (5)

• Slope filtrations revisited
• Classification of two dimensional split trianguline representations of $p$-adic fields
• Slope filtrations for relative Frobenius
• Deformations of trianguline B-pairs and Zariski density of two dimensional crystalline representations
• Sur la densité des représentations cristallines du groupe de Galois absolu de Q_p

Cited by in corpus (12)

• Deformations of trianguline B-pairs and Zariski density of two dimensional crystalline representations
• Density of potentially crystalline representations of fixed weight
• Cohomology of arithmetic families of (phi,Gamma)-modules
• On local Galois deformation rings
• Density of automorphic points in deformation rings of polarized global Galois representations
• $\mathcal{L}$-invariants, partially de Rham families and local-global compatibility
• Zariski density of crystalline representations for any p-adic field
• Companion points and locally analytic socle for ${\mathrm{GL}}_2(L)$
• Simple $\mathcal{L}$-invariants for ${\mathrm{GL}}_n$
• Iwasawa theory of de Rham (ϕ,Γ)-modules over the Robba rings
• Cohomology of $(\phi ,\tau )$-modules
• Sur un problème de compatibilité local-global localement analytique