Laurent Berger
Published 2013-07-01, updated 2014-04-21Version 3
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.
Comments: v3: some improvements, to appear in "Journal de l'\'Ecole polytechnique - Math\'ematiques". v2: some minor improvements
Ramification in C-extensions of local field of characteristic 0
On the U_p-operator in characteristic p
A Riemann Hypothesis for characteristic p L-functions
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