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The aim of this article is to study deformation theory of trianguline B-pairsfor any p-adic field. For benign B-pairs, a special good class of triangulineB-pairs, we prove a main theorem concerning tangent spaces of these deformationspaces. These are generalizations of Bellaiche-Chenevier's and Chenevier'sworks in the Q_p case, where they used (\phi,\Gamma)-modules over the Robbaring instead of using B-pairs. As an application of this theory, in the finalchapter, we prove a theorem concerning Zariski density of two dimensionalcrystalline representations for any p-adic field, which is a generalization ofColmez and Kisin's results in the Q_p case.

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