Geometry & Topology Monographs 3 (2000) - Invitation to higher local fields, Part I, section 12, pages 109-112

Two types of complete discrete valuation fields

M. Kurihara

Abstract. This work sketches the author classification of complete discrete valuation fields K of characteristic 0 with residue field of characteristic p into two classes depending on the behaviour of the torsion part of a differential module. For each of these classes, the quotient filtration of the Milnor K-groups of K is characterized for all sufficiently large members of the filtration, as a quotient of differential modules. For a higher local field the previous result and higher local class field theory imply certain restrictions on types of cyclic extensions of the field of sufficiently large degree.
Keywords. Complete discrete valuation fields, Milnor K-groups, differential forms.
AMS subject classification. 19F99, 19D99.

E-print: arXiv:math.NT/0012143

Masato Kurihara
Department of mathematics, Tokyo Metropolitan University, Minami-Osawa 1-1, Hachioji, Tokyo 192-03, Japan

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