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

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