Lifting the field of norms
Number Theory
2014-04-22 v3
Abstract
Let K be a finite extension of Q_p. The field of norms of a p-adic Lie extension K_infty/K is a local field of characteristic p which comes equipped with an action of Gal(K_infty/K). When can we lift this action to characteristic 0, along with a compatible Frobenius map? In this note, we formulate precisely this question, explain its relevance to the theory of (phi,Gamma)-modules, and give a condition for the existence of certain types of lifts.
Keywords
Cite
@article{arxiv.1307.0384,
title = {Lifting the field of norms},
author = {Laurent Berger},
journal= {arXiv preprint arXiv:1307.0384},
year = {2014}
}
Comments
v3: some improvements, to appear in "Journal de l'\'Ecole polytechnique - Math\'ematiques". v2: some minor improvements