Invitation to higher local fields, Interlude: Existence theorem for higher local class field theory
Number Theory
2009-09-25 v1 Algebraic Geometry
Abstract
Viewing higher local fields as ring objects in the category of iterated pro-ind-objects, a definition of open subgroups in Milnor K-groups of the fields is given. The self-duality of the additive group of a higher local field is proved. By studying norm groups of cohomological objects and using cohomological approach to higher local class field theory the existence theorem is proved.
Keywords
Cite
@article{arxiv.math/0012150,
title = {Invitation to higher local fields, Interlude: Existence theorem for higher local class field theory},
author = {Kazuya Kato},
journal= {arXiv preprint arXiv:math/0012150},
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-kato.abs.html