Geometry & Topology Monographs 3 (2000) -
Invitation to higher local fields,
pages 165-195
Existence theorem for higher local class field theory
K. Kato
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.
AMS subject classification. 19F05, 19F99, 11-99.
E-print: arXiv:math.NT/0012150
Kazuya Kato
Department of mathematics, University of Tokyo,
3-8-1- Meguro-ku Tokyo 153-8914, Tokyo, Japan
Email: kkato@ms.u-tokyo.ac.jp
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