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Grothendieck groups of complexes with null-homotopies

Published online by Cambridge University Press:  13 March 2014

Daniel Dugger
Daniel Dugger*
Affiliation:
Department of Mathematics, University of Oregon, Eugene, OR 97403, USA, [email protected]
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Abstract

This paper uses differential-graded methods to give a streamlined proof of a theorem of Foxby-Halvorson. The theorem states that certain relative K-groups made from complexes with bounded (but arbitrarily long) length coincide with similar K-groups in which one sets an absolute bound on the length of the complexes.

Keywords

Relative K-theorybounded complexes19A99
Type
Research Article
Information
Journal of K-Theory , Volume 13 , Issue 3 , June 2014 , pp. 517 - 531
Copyright
Copyright © ISOPP 2014 

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References

REFERENCES

A.Atiyah, M.F., K-theory, W.A. Benjamin, Inc., New York, 1967.Google Scholar
D.Dold, A., K-theory of non-additive functors of finite degree, Math. Ann. 196 (1972), 177–197.CrossRefGoogle Scholar
FH.Foxby, H.-B. and Halvorsen, E. B., Grothendieck groups for categories of complexes, J. K-theory 3(1) (2009), 165–203.CrossRefGoogle Scholar
TT.Thomason, R.W. and Trobaugh, T., Higher algebraic K-theory of schemes and of derived categories, The Grothendieck Festschrift 3, 246–435, Progr. Math. 88, Birkhäuser Boston, Boston, MA, 1990.Google Scholar
W.Weibel, C., The K-book. An introduction to algebraic K-theory. Graduate Studies in Mathematics 145. American Mathematical Society, Providence, RI, 2013.Google Scholar