Invitation to higher local fields, Part I, section 10: Explicit higher local class field theory

2000/12/18 by Ivan Fesenko
Mathematics · #math.NT #math.AG #msc:19F05 #msc:19F99 #msc:11-99

paper · pdf

published as Geom. Topol. Monogr. Volume 3(2000) 95-101 · 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-10.abs.html

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

Abstract

This is a presentation of explicit methods to construct higher local class field theory by using topological K-groups, explicit symbols and a generalization of Neukirch-Hazewinkel's axiomatic approaches. The existence theorem is discussed as well.

Related

• Invitation to higher local fields, Part I, section 1: Higher dimensional local fields
• Invitation to higher local fields, Part I, section 16: Higher class field theory without using K-groups
• An introduction to higher dimensional local fields and adeles
• Invitation to higher local fields, Part I, section 6: Topological Milnor K-groups of higher local fields
• Two-Dimensional Local-Global Class Field Theory in Positive Characteristic