Lifting the field of norms

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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Contributor : Laurent Berger <>
Submitted on : Wednesday, July 3, 2013 - 9:22:31 AM
Last modification on : Thursday, April 4, 2019 - 10:18:04 AM

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  • HAL Id : hal-00840755, version 1
  • ARXIV : 1307.0384



Laurent Berger. Lifting the field of norms. Journal de l'École polytechnique — Mathématiques, École polytechnique, 2014, 1, pp.29--38. 〈hal-00840755〉



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