Milnor \(K\)-groups modulo \(p^{n}\) of a complete discrete valuation field. (English) Zbl 1244.19002

Hiranouchi, Toshiro

Proc. Japan Acad., Ser. A 88, No. 4, 59-61 (2012).

For a mixed characteristic complete discrete valuation field \(K\) which contains a \(p^{n}\)-th root of unity, the author determines the graded quotients of the filtration on the Milnor \(K\)-groups \(K_{q}^{M}(K)\) modulo \(p^{n}\) in terms of differential forms of the residue field of \(K\).

Reviewer: L. N. Vaserstein (University Park)

MSC:

19D45

Higher symbols, Milnor \(K\)-theory

Keywords:

Milnor \(K\)-groups; complete discrete valuation field

References:

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