  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.
