Geodesic
On ramification theory in the~imperfect residue field case
Sbornik. Mathematics, Tome 194 (2003) no. 12, pp. 1747-1774

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This paper is devoted to the ramification theory of complete discrete valuation fields such that the residue field has prime characteristic $p$ and the cardinality of a $p$-base is 1. This class contains two-dimensional local and local-global fields. A new definition of ramification filtration for such fields is given. It turns out that Hasse–Herbrand type functions can be defined with all the usual properties. Thanks to this, a theory of upper ramification groups and the ramification theory of infinite extensions can be developed. The case of two-dimensional local fields of equal characteristic is studied in detail. A filtration on the second $K$-group of the field in question is introduced that is different from the one induced by the standard filtration on the multiplicative group. The reciprocity map of two-dimensional local class field theory is proved to identify this filtration with the ramification filtration. 
@article{SM_2003_194_12_a0,
     author = {I. B. Zhukov},
     title = {On ramification theory in the~imperfect residue field case},
     journal = {Sbornik. Mathematics},
     pages = {1747--1774},
     publisher = {mathdoc},
     volume = {194},
     number = {12},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2003_194_12_a0/}
}
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I. B. Zhukov. On ramification theory in the~imperfect residue field case. Sbornik. Mathematics, Tome 194 (2003) no. 12, pp. 1747-1774. http://geodesic.mathdoc.fr/item/SM_2003_194_12_a0/