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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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On relative and bi-relative algebraic $K$-theory of rings of finite characteristic
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by Thomas Geisser and Lars Hesselholt PDF
J. Amer. Math. Soc. 24 (2011), 29-49 Request permission


We consider unital associative rings in which a fixed prime number $p$ is nilpotent. It was proved long ago by Weibel that for such rings, the relative $K$-groups associated with a nilpotent extension and the bi-relative $K$-groups associated with a pull-back square are $p$-primary torsion groups. However, the question of whether these groups can contain a $p$-divisible torsion subgroup has remained an open and intractable problem. In this paper, we answer this question in the negative. In effect, we prove the stronger statement that the groups in question are always $p$-primary torsion groups of bounded exponent.
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Additional Information
  • Thomas Geisser
  • Affiliation: Department of Mathematics, University of Southern California, 3620 Vermont Avenue KAP 108, Los Angeles, California 90089
  • Email:
  • Lars Hesselholt
  • Affiliation: Graduate School of Mathematics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8602 Japan
  • MR Author ID: 329414
  • Email:
  • Received by editor(s): February 18, 2009
  • Received by editor(s) in revised form: July 23, 2010
  • Published electronically: September 15, 2010
  • Additional Notes: The authors were supported in part by NSF Grant Nos. 0901021 and 0306519.
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 24 (2011), 29-49
  • MSC (2010): Primary 19D55; Secondary 18G50, 16S70
  • DOI:
  • MathSciNet review: 2726598