On the Milnor -groups of complete discrete valuation fields

  • Jinya Nakamura

    Graduate School of Mathematical Sciences University of Tokyo Komaba, Meguro-ku Tokyo, Japan
On the Milnor $K$-groups of complete discrete valuation fields cover
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Abstract

For a discrete valuation field , the unit group of 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 -group is a generalization of the unit group, and it also has a natural decreasing filtration. However, if 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.

Cite this article

Jinya Nakamura, On the Milnor -groups of complete discrete valuation fields. Doc. Math. 5 (2000), pp. 151–200

DOI 10.4171/DM/78