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

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

2010-06-25

arxiv.org/abs/1006.4891v4

Mathematics

Number Theory

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

Scientific paper

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 (\phi,\Gamma)-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.

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