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

Kurihara, Masato

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

Pour un exemple typique de corps de valuation discrète complet $K$ de type II au sens de [12], nous déterminons les quotients gradués ${gr}^i{K}_2\left(K\right)$ 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 ${gr}^i{K}_2\left(K\right)$ 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.

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