## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### Milnor $K$-groups modulo $p^{n}$ of a complete discrete valuation field

Toshiro Hiranouchi

#### Abstract

For a mixed characteristic complete discrete valuation field $K$ which contains a $p^{n}$-th root of unity, we determine 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 $K$.

#### Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 88, Number 4 (2012), 59-61.

Dates
First available in Project Euclid: 5 April 2012

https://projecteuclid.org/euclid.pja/1333631994

Digital Object Identifier
doi:10.3792/pjaa.88.59

Mathematical Reviews number (MathSciNet)
MR2912843

Zentralblatt MATH identifier
1244.19002

#### Citation

Hiranouchi, Toshiro. Milnor $K$-groups modulo $p^{n}$ of a complete discrete valuation field. Proc. Japan Acad. Ser. A Math. Sci. 88 (2012), no. 4, 59--61. doi:10.3792/pjaa.88.59. https://projecteuclid.org/euclid.pja/1333631994

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