On the K-theory of division algebras over local fields

  • Lars HesselholtEmail author
  • Michael Larsen
  • Ayelet Lindenstrauss


Let K be a complete discrete valuation field with finite residue field of characteristic p, and let D be a central division algebra over K of finite index d. Thirty years ago, Suslin and Yufryakov [ 35, Theorem 3] showed that for all prime numbers \(\ell \ne p\)



We gratefully acknowledge the generous assistance that we have received from a DNRF Niels Bohr Professorship, Simons Foundation Grant 359565, and NSF Grants DMS-1702152 and DMS-1552766. The first author also thanks Indiana University and the Hausdorff Research Institute for Mathematics in Bonn for their hospitality and support, and the second and third author thank the University of Copenhagen for its hospitality and support. The first author further thanks Thomas Geisser for helpful discussions. We are much indebted to Jacob Lurie for pointing out a mistake in an earlier version of the work presented here, and finally, we thank an anonymous referee for many very helpful remarks.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019
corrected publication 2019

Authors and Affiliations

  • Lars Hesselholt
    • 1
    • 2
    Email author
  • Michael Larsen
    • 3
  • Ayelet Lindenstrauss
    • 3
  1. 1.Nagoya UniversityNagoyaJapan
  2. 2.University of CopenhagenCopenhagenDenmark
  3. 3.Indiana UniversityBloomingtonUSA

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