Generalised Kawada-Satake method for Mackey functors in class field theory
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 simplif...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Springer
2018
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| Online Access: | https://eprints.nottingham.ac.uk/47756/ |
| _version_ | 1848797622444228608 |
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| author | Fesenko, Ivan Vostokov, Sergei V. Yoon, Seok Ho |
| author_facet | Fesenko, Ivan Vostokov, Sergei V. Yoon, Seok Ho |
| author_sort | Fesenko, Ivan |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:06:48Z |
| format | Article |
| id | nottingham-47756 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:06:48Z |
| publishDate | 2018 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-477562019-04-23T04:30:13Z https://eprints.nottingham.ac.uk/47756/ Generalised Kawada-Satake method for Mackey functors in class field theory Fesenko, Ivan Vostokov, Sergei V. Yoon, Seok Ho 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. Springer 2018-09-30 Article PeerReviewed application/pdf en https://eprints.nottingham.ac.uk/47756/1/ksm.pdf Fesenko, Ivan, Vostokov, Sergei V. and Yoon, Seok Ho (2018) Generalised Kawada-Satake method for Mackey functors in class field theory. European Journal of Mathematics, 4 (3). pp. 953-987. ISSN 2199-6768 Class field theory; Higher class field theory; Kawada-Satake theory; Mackey functors https://link.springer.com/article/10.1007%2Fs40879-018-0245-x doi:10.1007/s40879-018-0245-x doi:10.1007/s40879-018-0245-x |
| spellingShingle | Class field theory; Higher class field theory; Kawada-Satake theory; Mackey functors Fesenko, Ivan Vostokov, Sergei V. Yoon, Seok Ho Generalised Kawada-Satake method for Mackey functors in class field theory |
| title | Generalised Kawada-Satake method for Mackey functors in class field theory |
| title_full | Generalised Kawada-Satake method for Mackey functors in class field theory |
| title_fullStr | Generalised Kawada-Satake method for Mackey functors in class field theory |
| title_full_unstemmed | Generalised Kawada-Satake method for Mackey functors in class field theory |
| title_short | Generalised Kawada-Satake method for Mackey functors in class field theory |
| title_sort | generalised kawada-satake method for mackey functors in class field theory |
| topic | Class field theory; Higher class field theory; Kawada-Satake theory; Mackey functors |
| url | https://eprints.nottingham.ac.uk/47756/ https://eprints.nottingham.ac.uk/47756/ https://eprints.nottingham.ac.uk/47756/ |