#### DOCUMENTA MATHEMATICA, Vol. Extra Volume: John H. Coates' Sixtieth Birthday (2006), 685-709

Anthony J. Scholl

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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