Invitation to higher local fields, Part I, section 12: Two types of complete discrete valuation fields

Details Invitation to higher local fields, Part I, section 12: Two types of complete discrete valuation fields Invitation to higher local fields, Part I, section 12: Two types of complete discrete valuation fields

2000-12-18

arxiv.org/abs/math/0012143v1

Geom. Topol. Monogr. Volume 3(2000) 109-112

Mathematics

Number Theory

For introduction and notation, see math.NT/0012131 . Published by Geometry and Topology Monographs at http://www.maths.warwi

Scientific paper

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.

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