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 <ibz@math.nott.ac.uk, zhukov@pdmi.ras.ru>