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On the Equivalence of Quillen's and Swan's K -Theories

On the Equivalence of Quillen's and Swan's K -Theories The K -theory of rings can be defined in terms of nonabelian derived functors as described in Nonabelian derived functors and algebraic K-theory. Springer, 1973; see also the books Algebraic K-theory. Kluwer Academic Publishers Group, 1995 and Non-abelian homological algebra and its applications. Kluwer Academic Publishers, 1997 of Inassaridze for a similar approach. In fact both Swan's theory and Quillen's theory can be described this way. The equivalence of both K -theories is proved by Gersten Comm. Algebra 1: 39–64, 1974. In this paper we give a proof using these descriptions that involve nonabelian derived functors. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

On the Equivalence of Quillen's and Swan's K -Theories

Georgian Mathematical Journal , Volume 9 (4) – Dec 1, 2002

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Publisher
de Gruyter
Copyright
© Heldermann Verlag
ISSN
1072-947X
eISSN
1072-9176
DOI
10.1515/GMJ.2002.691
Publisher site
See Article on Publisher Site

Abstract

The K -theory of rings can be defined in terms of nonabelian derived functors as described in Nonabelian derived functors and algebraic K-theory. Springer, 1973; see also the books Algebraic K-theory. Kluwer Academic Publishers Group, 1995 and Non-abelian homological algebra and its applications. Kluwer Academic Publishers, 1997 of Inassaridze for a similar approach. In fact both Swan's theory and Quillen's theory can be described this way. The equivalence of both K -theories is proved by Gersten Comm. Algebra 1: 39–64, 1974. In this paper we give a proof using these descriptions that involve nonabelian derived functors.

Journal

Georgian Mathematical Journalde Gruyter

Published: Dec 1, 2002

Keywords: Higher algebraic K -theory; simplicial resolutions

There are no references for this article.