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Finite K-theory spaces

Published online by Cambridge University Press:  05 September 2005

DOMINIQUE ARLETTAZ  and
HVEDRI INASSARIDZE
DOMINIQUE ARLETTAZ
Affiliation:
Université de Lausanne, IGAT-BCH, 1015-Lausanne, Switzerland. e-mail: [email protected]
HVEDRI INASSARIDZE
Affiliation:
A. Razmadze Mathematical Institute, Georgian Academy of Sciences, Tbilisi, Georgia. e-mail: [email protected]
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Abstract

This paper presents some new results on algebraic K-theory with finite coefficients. The argument is based on a topological construction of a space $F_mK(R)$, for any ring $R$ and any integer $m\geq 2$, having the property that the ordinary homotopy theory of $F_mK(R)$ is isomorphic to the algebraic K-theory of $R$ with coefficients in $\bb {Z}/m$: $\pi_n(F_mK(R))\cong K_n(R;\bb {Z}/m)$ for $n\geq 1$. This space $F_mK(R)$ is called the $\mod m$ K-theory space of $R$. The paper is devoted to the investigation of several properties of the groups $K_n(R;\bb {Z}/m)$, for $n\in\bb {Z}$, and to some calculations of the integral homology of finite K-theory spaces.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 139 , Issue 2 , September 2005 , pp. 261 - 286
Copyright
2005 Cambridge Philosophical Society

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