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

Full text: dvi.gz 57 k, dvi 136 k, ps.gz 1009 k, pdf 282 k.


Home Page of DOCUMENTA MATHEMATICA