Invitation to higher local fields, Interlude: Existence theorem for higher local class field theory

Details Invitation to higher local fields, Interlude: Existence theorem for higher local class field theory Invitation to higher local fields, Interlude: Existence theorem for higher local class field theory

2000-12-18

arxiv.org/abs/math/0012150v1

Geom. Topol. Monogr. Volume 3(2000) 165-195

Mathematics

Number Theory

For introduction and notation, see math.NT/0012131 . Published by Geometry and Topology Monographs at http://www.maths.warwi

Scientific paper

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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