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

Kurihara, Masato

doi:10.5802/jtnb.452

On the structure of Milnor

K

-groups of certain complete discrete valuation fields

Kurihara, Masato ¹

¹ Department of Mathematics, Tokyo Metropolitan University, Hachioji, Tokyo, 192-03, Japan

Journal de théorie des nombres de Bordeaux, Tome 16 (2004) no. 2, pp. 377-401.

Résumé
Abstract

Pour un exemple typique de corps de valuation discrète complet $K$ de type II au sens de [12], nous déterminons les quotients gradués ${gr}^{i} K_{2} (K)$ pour tout $i > 0$ . Dans l’appendice, nous décrivons les $K$ -groupes de Milnor d’un certain anneau local à l’aide de modules de différentielles, qui sont liés à la théorie de la cohomologie syntomique.

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.

MR Zbl

DOI : 10.5802/jtnb.452

Affiliations des auteurs :

Kurihara, Masato ¹

¹ Department of Mathematics, Tokyo Metropolitan University, Hachioji, Tokyo, 192-03, Japan

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Kurihara, Masato. On the structure of Milnor $K$-groups of certain complete discrete valuation fields. Journal de théorie des nombres de Bordeaux, Tome 16 (2004) no. 2, pp. 377-401. doi : 10.5802/jtnb.452. https://www.numdam.org/articles/10.5802/jtnb.452/

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Hiranouchi, Toshiro Milnor $K$ -groups modulo $p^{n}$ of a complete discrete valuation field, Proceedings of the Japan Academy, Series A, Mathematical Sciences, Volume 88 (2012) no. 4 | DOI:10.3792/pjaa.88.59
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Nakamura, Jinya, Invitation to higher local fields (2000), p. 123 | DOI:10.2140/gtm.2000.3.123

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