Volume 3 (2000)

Download this article
For printing
Recent Volumes
Volume 1, 1998
Volume 2, 1999
Volume 3, 2000
Volume 4, 2002
Volume 5, 2002
Volume 6, 2003
Volume 7, 2004
Volume 8, 2006
Volume 9, 2006
Volume 10, 2007
Volume 11, 2007
Volume 12, 2007
Volume 13, 2008
Volume 14, 2008
Volume 15, 2008
Volume 16, 2009
Volume 17, 2011
Volume 18, 2012
Volume 19, 2015
The Series
MSP Books and Monographs
About this Series
Editorial Board
Ethics Statement
Author Index
Submission Guidelines
Author Copyright Form
Purchases
ISSN (electronic): 1464-8997
ISSN (print): 1464-8989
Other MSP Publications

Existence theorem for higher local fields

Kazuya Kato

Geometry & Topology Monographs 3 (2000) 165–195

DOI: 10.2140/gtm.2000.3.165

arXiv: math.NT/0012150

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

higher local class field theory, existence theorem

Mathematical Subject Classification

Primary: 11-99, 19F05, 19F99

References
Publication


Published: 10 December 2000

Authors
Kazuya Kato
Department of Mathematics
University of Tokyo
3-8-1 Komaba Meguro-Ku
Tokyo 153-8914
Japan