  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.
