This work sketches the author classification of complete discrete valuation fields K of
characteristic 0 with residue field of characteristic p into two classes depending on the
behaviour of the torsion part of a differential module. For each of these classes, the
quotient filtration of the Milnor K–groups of K is characterized for all sufficiently
large members of the filtration, as a quotient of differential modules. For a
higher local field the previous result and higher local class field theory imply
certain restrictions on types of cyclic extensions of the field of sufficiently large
degree.
Keywords
complete discrete valuation fields,
Milnor K–groups, differential forms