Higher Fields of Norms and (phi,Gamma)-Modules

We describe a generalisation of the Fontaine-Wintenberger theory of the ``field of norms'' functor to local fields with imperfect residue field, generalising work of Abrashkin for higher dimensional local fields. We also compute the cohomology of associated $p$-adic Galois representations using $(\phi,\Gamma)$-modules.

2000 Mathematics Subject Classification: 11S15, 11S23, 11S25, 12G05

Keywords and Phrases: local fields, ramification theory, Galois representations

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