Higher fields of norms and -modules

  • Anthony J. Scholl

    Department of Pure Mathematics and Mathematical Statistics (DPMMS), University of Cambridge, Cambridge, England


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 -adic Galois representations using -modules.