An analogue of the field-of-norms functor and of the Grothendieck Conjecture.

Abstract

The paper contains a construction of an analogue of the Fontaine-Wintenberger field-of-norms functor for higher-dimensional local fields. This construction is done completely in terms of the ramification theory of such fields. It is applied to deduce the mixed characteristic case of a local analogue of the Grothendieck conjecture for these fields from its characteristic $ p$ case, which was proved earlier by the author.