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On relative and bi-relative algebraic $K$-theory of rings of finite characteristic

Authors: Thomas Geisser and Lars Hesselholt
Journal: J. Amer. Math. Soc. 24 (2011), 29-49
MSC (2010): Primary 19D55; Secondary 18G50, 16S70
Published electronically: September 15, 2010
MathSciNet review: 2726598
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Abstract: 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

Lars Hesselholt
Affiliation: Graduate School of Mathematics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8602 Japan
MR Author ID: 329414

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.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.