arXiv Analytics

Sign in

arXiv:math/0012150 [math.NT]AbstractReferencesReviewsResources

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

Kazuya Kato

Published 2000-12-18Version 1

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.

Comments: For introduction and notation, see math.NT/0012131 . Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon3/m3-I-kato.abs.html
Journal: Geom. Topol. Monogr. Volume 3(2000) 165-195
Categories: math.NT, math.AG
Subjects: 19F05, 19F99, 11-99
Related articles: Most relevant | Search more
arXiv:math/0012136 [math.NT] (Published 2000-12-18)
Invitation to higher local fields, Part I, section 5: Kato's higher local class field theory
arXiv:math/0012141 [math.NT] (Published 2000-12-18)
Invitation to higher local fields, Part I, section 10: Explicit higher local class field theory
arXiv:math/0012138 [math.NT] (Published 2000-12-18)
Invitation to higher local fields, Part I, section 7: Parshin's higher local class field theory in characteristic p

Links

Toolbox