Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-17T16:57:53.627Z Has data issue: false hasContentIssue false

Relative reciprocities on Dedekind domains

Published online by Cambridge University Press:  03 June 2013

Frans Keune*
Affiliation:
Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen, P.O. Box 9010, 6500 GL Nijmegen, The [email protected]
Get access

Abstract

Exact sequences in algebraic K-theory contain a lot of information. Here it is shown that by using K-theory exact sequences one can easily derive Bass’ description [1] of the SK1 of an ideal in a Dedekind domain in terms of relative reciprocities.

Type
Research Article
Copyright
Copyright © ISOPP 2013 

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

1.Bass, H., Algebraic K-Theory. New York: Benjamin 1968Google Scholar
2.Bass, H. and Tate, J., The Milnor ring of a global field. Algebraic K-Theory II, 349446. Lecture Notes in Mathematics 342. Berlin-Heidelberg-New York: Springer 1973Google Scholar
3.Keune, F., (t2 – t)-reciprocities on the affine line and Matsumoto's theorem, Inventiones math. 28 (1975), 185192Google Scholar
4.Keune, F., The relativization of K2, J. Algebra 54 (1978), 159177CrossRefGoogle Scholar
5.Maazen, H. and Stienstra, J., A Presentation for K 2 of split radical pairs, Journal of Pure and Applied Algebra 10 (1977), 271294Google Scholar
6.Matsumoto, H., Sur les sous-groupes arithmétique des groupes semi-simples déployés, Ann. Sci. Ec. Norm. Sup. 4e série 2 (1969), 162Google Scholar
7.Milnor, J., An Introduction to Algebraic K-Theory. Princeton: Princeton University Press 1971Google Scholar
8.Quillen, D., Higher algebraic K-theory, in Algebraic K-Theory, Vol. I, Lecture Notes in Mathematics 341, Springer-Verlag, Berlin 1973Google Scholar