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

European Journal of Mathematics volume 4, pages 953–987 (2018)Cite this article

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.

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Acknowledgements

It is our great pleasure to dedicate this paper to Sasha Beilinson whose inspirational mathematical vision and work are beautifully complemented by his compassion, openness and kindness.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK

    Ivan B. Fesenko & Seok Ho Yoon

  2. Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskaya nab., 79, 199034, St. Petersburg, Russia

    Sergei V. Vostokov

Authors
  1. Ivan B. Fesenko
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  2. Sergei V. Vostokov
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  3. Seok Ho Yoon
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Corresponding author

Correspondence to Ivan B. Fesenko.

Additional information

To Sasha Beilinson on the occasion of his 60th birthday

Work on this paper was partially supported by EPSRC programme Grant ‘Symmetries and Correspondences’ EP/M024830.

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

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  • DOI: https://doi.org/10.1007/s40879-018-0245-x

Keywords

  • Class field theory
  • Higher fields
  • Higher class field theory
  • Witt vectors
  • Reflexivity for non-locally compact groups

Mathematics Subject Classification

  • 19F05
  • 13F35
  • 46B10