Deformations of Trianguline B-Pairs and Zariski Density of Two Dimensional Crystalline Representations
Vol. 20 (2013), No. 4, Page 461–568.
Nakamura, Kentaro
Deformations of Trianguline B-Pairs and Zariski Density of Two Dimensional Crystalline Representations
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Abstract:
The aims of this article are to study the deformation theory of trianguline B-pairs and to construct a p-adic family of two dimensional trianguline representations for any p-adic field. The deformation theory is the generalization of Bella\"iche-Chenevier's and Chenevier's works in the Qp-case, where they used (φ,Γ)-modules over the Robba ring instead of using B-pairs. Generalizing and modifying Kisin's theory of Xfs for any p-adic field, we construct a p-adic family of two dimensional trianguline representations. As an application of these theories, we prove a theorem concerning the Zariski density of two dimensional crystalline representations for any p-adic field, which is a generalization of Colmez's and Kisin's theorem for the Qp-case.
Keywords: p-adic Hodge theory, trianguline representations, B-pairs.
Mathematics Subject Classification (2010): Primary 11F80; Secondary 11F85, 11S25.
Mathematical Reviews Number: MR3185293
Received: 2013-06-13
