Invitation to higher local fields, Part I, section 6: Topological Milnor K-groups of higher local fields

2000/12/18 by Ivan Fesenko
Mathematics · #math.NT #math.AG #msc:54E99 #msc:19D99 #msc:46A45 #msc:19F15

paper · pdf

published as Geom. Topol. Monogr. Volume 3(2000) 61-74 · 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-6.abs.html

arxiv created 2000/12/18 · arxiv updated 2009/11/30

Abstract

Certain topologies on Milnor K-groups of higher local fields K are studied. These are related to the topology on the multiplicative group and important for explicit higher local class field theory. The structure of the quotient of Milnor K-groups modulo the intersection of all neighbourhoods of zero is described.

Related

• Invitation to higher local fields, Part I, section 1: Higher dimensional local fields
• Invitation to higher local fields, Part I, section 10: Explicit higher local class field theory
• Invitation to higher local fields, Part I, section 2: p-primary part of the Milnor K-groups and Galois cohomology of fields of characteristic p
• Geometric presentations of Milnor K-groups of certain Artin algebras and Bass-Tate-Kato norms
• Milnor-Witt K-groups of local rings