On the structure of Milnor K -groups of certain complete discrete valuation fields

For a typical example of a complete discrete valuation field K of type II in the sense of [12], we determine the graded quotients gr i K 2 ( K ) for all i > 0 . In the Appendix, we describe the Milnor K -groups of a certain local ring by using differential modules, which are related to the theory of syntomic cohomology.