Lifting the field of norms

2013/07/01 by Laurent Berger, Berger, Laurent · 1 citation
Mathematics · #11S15 #11S20 #11S25 #11S31 #11S82 #13F25 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11S15 #msc:11S20 #msc:11S25 #msc:11S31 #msc:11S82 #msc:13F25

paper · pdf · doi:10.48550/arxiv.1307.0384

v3: some improvements, to appear in "Journal de l'École polytechnique - Mathématiques". v2: some minor improvements

arxiv created 2014/04/21 · arxiv updated 2014/04/22

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.

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• Multivariable period rings of p-adic false Tate curve extension

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