On ramification theory in the imperfect residue field case, by Igor B. Zhukov
We consider the class of complete discrete valuation fields such that the residue
field is of prime charactersitic p and the cardinality of a p-base is 1. This class
includes two-dimensional local and local-global fields. A new definition of ramification
filtration for such fields is given. It appears that a Hasse-Herbrand type functions can
be defined with all the usual properties. Therefore, a theory of upper ramification
groups, as well as the ramification theory of infinite extensions, can be developed.
Next, we consider an equal characteristic two-dimensional local field K. We introduce some
filtration on the second K-group of a given field. This filtration is other than the filtartion
induced by the valuation. We prove that the reciprocity map of two-dimensional local class
field theory identifies this filtrartion with the ramification filtration.
Igor B. Zhukov <firstname.lastname@example.org, email@example.com>