Geodesic
On the Milnor $K$-groups of complete discrete valuation fields
Documenta mathematica, Tome 5 (2000), pp. 151-200
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For a discrete valuation field K, the unit group K× of K has a natural decreasing filtration with respect to the valuation, and the graded quotients of this filtration are given in terms of the residue field. The Milnor K-group KqM​(K) is a generalization of the unit group, and it also has a natural decreasing filtration. However, if K is of mixed characteristics and has an absolute ramification index greater than one, the graded quotients of this filtration are not yet known except in some special cases.
DOI : 10.4171/dm/78
Classification : 11S70, 19D45
Mots-clés : the Milnor K-group, complete discrete valuation field, higher local class field theory 
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     author = {Jinya Nakamura},
     title = {On the {Milnor} $K$-groups of complete discrete valuation fields},
     journal = {Documenta mathematica},
     pages = {151--200},
     year = {2000},
     volume = {5},
     doi = {10.4171/dm/78},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/78/}
}
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Jinya Nakamura. On the Milnor $K$-groups of complete discrete valuation fields. Documenta mathematica, Tome 5 (2000), pp. 151-200. doi: 10.4171/dm/78

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