Hostname: page-component-7479d7b7d-fwgfc Total loading time: 0 Render date: 2024-07-13T04:39:19.847Z Has data issue: false hasContentIssue false
  • English
  • Français

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, ddugger@uoregon.edu
Get access

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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