Crystalline and semi-stable representations in the imperfect residue field case
Number Theory
2012-11-19 v2
Abstract
Let K be a p-adic local field with residue field k such that [k:k^p]=p^e<\infty and V be a p-adic representation of Gal(\bar{K}/K). Then, by using the theory of p-adic differential modules, we show that V is a potentially crystalline (resp. potentially semi-stable) representation of Gal(\bar{K}/K) if and only if V is a potentially crystalline (resp. potentially semi-stable) representation of Gal(\bar{K^{pf}}/K^{pf}) where K^{pf}/K is a certain p-adic local field whose residue field is the smallest perfect field k^{pf} containing k. As an application, we prove the p-adic monodromy theorem of Fontaine in the imperfect residue field case.
Keywords
Cite
@article{arxiv.1105.0846,
title = {Crystalline and semi-stable representations in the imperfect residue field case},
author = {Kazuma Morita},
journal= {arXiv preprint arXiv:1105.0846},
year = {2012}
}