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Existence theorem for higher local fields
Kazuya Kato
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Geometry & Topology Monographs 3
(2000) 165–195
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Abstract
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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.
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Keywords
higher local class field theory,
existence theorem
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Mathematical Subject Classification
Primary: 11-99, 19F05, 19F99
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Publication
Published: 10 December 2000
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