2,617 research outputs found
Zariski density of crystalline representations for any p-adic field
The aim of this article is to prove Zariski density of crystalline
representations in the rigid analytic space associated to the universal
deformation ring of a d-dimensional mod p representation of Gal(\bar{K}/K) for
any d and for any p-adic field K. This is a generalization of the results of
Colmez, Kisin (d=2, K=Q_p), of the author (d=2, any K), of Chenevier (any d,
K=Q_p). A key ingredient for the proof is to construct a p-adic family of
trianguline representations. In this article, we construct (an approximation
of) this family by generalizing Kisin's theory of finite slope subspace X_{fs}
for any d and for any K
Deformations of trianguline B-pairs
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 case of K=Q_p, where they used (phi,Gamma)-modules over Robba ring
instead of using B-pairs. The main theorem, the author hopes, will play crucial
roles in some problems of Zariski density of modular points or of crystalline
points in deformation spaces of global or local p-adic Galois representations.Comment: 30page
Deformations of trianguline B-pairs and Zariski density of two dimensional crystalline representations
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.Comment: 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 representation
Zeta morphisms for rank two universal deformations (Automorphic forms, Automorphic representations, Galois representations, and its related topics)
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