Zariski density of crystalline representations for any p-adic field
Number Theory
2013-11-26 v4
Abstract
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.
Keywords
Cite
@article{arxiv.1104.1760,
title = {Zariski density of crystalline representations for any p-adic field},
author = {Kentaro Nakamura},
journal= {arXiv preprint arXiv:1104.1760},
year = {2013}
}