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
Email: m-kuri@comp.metro-u.ac.jp
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