Generalised Kawada-Satake method for Mackey functors in class field theory

Fesenko, Ivan; Vostokov, Sergei V.; Yoon, Seok Ho

Abstract

We propose and study a generalised Kawada--Satake method for Mackey functors in the class field theory of positive characteristic. The root of this method is in the use of explicit pairings, such as the Artin--Schreier--Witt pairing, for groups describing abelian extensions. We separate and simplify the algebraic component of the method and discuss a relation between the existence theorem in class field theory and topological reflexivity with respect to the explicit pairing. We apply this method to derive higher local class field theory of positive characteristic, using advanced properties of topological Milnor K-groups of such fields.

Citation

Fesenko, I., Vostokov, S. V., & Yoon, S. H. (2018). Generalised Kawada-Satake method for Mackey functors in class field theory. European Journal of Mathematics, 4(3), 953–987. https://doi.org/10.1007/s40879-018-0245-x

• Journal Article Type: Article
• Acceptance Date: Apr 8, 2018
• Online Publication Date: Apr 23, 2018
• Publication Date: Sep 30, 2018
• Deposit Date: Apr 9, 2018
• Publicly Available Date: Apr 24, 2019
• Journal: European Journal of Mathematics
• Electronic ISSN: 2199-675X
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 4
• Issue: 3
• Pages: 953–987
• DOI: https://doi.org/10.1007/s40879-018-0245-x
• Keywords: Class field theory; Higher class field theory; Kawada-Satake theory; Mackey functors
• Public URL: https://nottingham-repository.worktribe.com/output/927576
• Publisher URL: https://link.springer.com/article/10.1007%2Fs40879-018-0245-x
• Additional Information: This is a post-peer-review, pre-copyedit version of an article published in European Journal of Mathematics. The final authenticated version is available online at: http://dx.doi.org/10.1007/s40879-018-0245-x
• Contract Date: Apr 9, 2018