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

Geisser, Thomas; Hesselholt, Lars

doi:10.1090/S0894-0347-2010-00682-0

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On relative and bi-relative algebraic -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
Posted: September 15, 2010
MathSciNet review: 2726598
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Abstract: We consider unital associative rings in which a fixed prime number is nilpotent. It was proved long ago by Weibel that for such rings, the relative -groups associated with a nilpotent extension and the bi-relative -groups associated with a pull-back square are -primary torsion groups. However, the question of whether these groups can contain a -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 -primary torsion groups of bounded exponent.

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