On the Structures of the Milnor K-Groups of Some Complete Discrete Valuation Fields |
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Authors: | Jinya Nakamura |
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Affiliation: | (1) Graduate School of Mathematical Sciences, University of Tokyo, 3–8–1 Komaba Meguro–ku, Tokyo, 153–8914, Japan |
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Abstract: | For a complete discrete valuation field K, the unit group of K has a natural decreasing filtration with respect to the valuation, and the graded quotients of this filtration are written in terms of the residue field. The Milnor K-group of a field is a generalization of the unit group. The Milnor K-group of K has a natural decreasing filtration of the same kind. However, if K is of mixed characteristics and has an absolute ramification index greater than one, the structure is not yet known. The aim of this paper is to determine the structure of the Milnor K-group of some special K, which are of mixed characteristics (0,p), whose residue fields are allowed to be imperfect, and which are of absolute ramification index p(p–1). |
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Keywords: | Milnor K-group complete discrete valuation field. |
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