Zariski density of crystalline representations for any p-adic field

2011/04/10 by Kentaro Nakamura, Nakamura, Kentaro
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Alkaloids: synthesis and pharmacology

paper · doi:10.48550/arxiv.1104.1760

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(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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