English

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

Number Theory 2009-09-25 v1 Algebraic Geometry

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

Cite

@article{arxiv.math/0012143,
  title  = {Invitation to higher local fields, Part I, section 12: Two types of complete discrete valuation fields},
  author = {Masato Kurihara},
  journal= {arXiv preprint arXiv:math/0012143},
  year   = {2009}
}

Comments

For introduction and notation, see math.NT/0012131 . Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon3/m3-I-12.abs.html