Scholl, Anthony J.

Higher fields of norms and $(\varphi,\Gamma)$-modules

Doc. Math. (Bielefeld) Extra Vol. John H. Coates' Sixtieth Birthday, 685-709 (2006)


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.

Mathematics Subject Classification

11S15, 11S23, 11S25, 12G05


local fields, ramification theory, Galois representations