Zariski density of crystalline representations for any p-adic field

Details Zariski density of crystalline representations for any p-adic field Zariski density of crystalline representations for any p-adic field

2011-04-10

arxiv.org/abs/1104.1760v3

Mathematics

Number Theory

Scientific paper

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.

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