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Bott Periodicity for group rings An Appendix to “Periodicity of Hermitian K-groups”

Published online by Cambridge University Press:  24 May 2011

Charles Weibel
Charles Weibel
Affiliation:
Department of Mathematics, Rutgers University, Piscataway, NJ 08854, [email protected]
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Abstract

We show that the groups Kn(RG;ℤ/m) are Bott-periodic for n ≥ 1 whenever G is a finite group, m is prime to |G|, R is a ring of S-integers in a number field and 1/m ∊ R.

Keywords

algebraic K-theoryBott periodicitygroup ring
Type
Research Article
Information
Journal of K-Theory , Volume 7 , Issue 3 , June 2011 , pp. 495 - 498
Copyright
Copyright © ISOPP 2011

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References

BKO.Berrick, A. J., Karoubi, M. and Østvaer, P. A., Periodicity of hermitian K-groups, J. K-Theory 7 (2011), to appear.CrossRefGoogle Scholar
1.Browder, W., Algebraic K-theory with coefficients ℤ/p, pp. 40–84 in Lecture Notes in Math. 657, Springer-Verlag, 1978.Google Scholar
2.Curtis, C. and Reiner, I., Methods of Representation Theory, Wiley & Sons, New York, 1981.Google Scholar
3.Gabber, O., K-theory of Henselian local rings and Henselian pairs, AMS Contemp. Math. 126 (1992), 59–70.CrossRefGoogle Scholar
4.Hesselholt, L. and Madsen, I., Cyclic polytopes and the K-theory of truncated polynomial algebras, Invent. Math. 130 (1997), 73–97.CrossRefGoogle Scholar
5.Hornbostel, J. and Yagunov, S., Rigidity for Henselian local rings and 1-representable theories, Math. Zeit. 255 (2007), 437–449.CrossRefGoogle Scholar
6.Voevodsky, V., Motivic cohomology with ℤ/2 coefficients, Publ. Math. Inst. Hautes Études Sci. 98 (2003), 59–104.CrossRefGoogle Scholar
7.Suslin, A. and Yufryakov, A., The K-theory of local division algebras. (Russian) Dokl. Akad. Nauk SSSR 288 (1986), 832–836. English Transl. Soviet Math. Dokl. 33 (1986), 794–798.Google Scholar
8.Weibel, C., Mayer-Vietoris sequences and module structures on NK*, pp. 466–493 in Lecture Notes in Math. 854, Springer-Verlag, 1981.Google Scholar
9.Weibel, C., Mayer-Vietoris sequences and mod p K-theory, pp. 390–407 in Lecture Notes in Math. 966, Springer-Verlag, 1982.Google Scholar
10.Weibel, C., Homotopy algebraic K-theory, AMS Contemp Math. 83 (1989), 461–488.CrossRefGoogle Scholar
11.Weibel, C., Algebraic K-theory of rings of integers in local and global fields, chapter 5 (pp. 139–190) in Handbook of K-theory, Springer-Verlag, 2005. Archived at http://www.math.uiuc.edu/K-theory/0981/book/1-139-190.pdfCrossRefGoogle Scholar
12.Weibel, C., The Norm Residue Isomorphism Theorem, J. Topology 2 (2009), 346–372.CrossRefGoogle Scholar