Hostname: page-component-77c89778f8-gq7q9 Total loading time: 0 Render date: 2024-07-16T12:05:17.139Z Has data issue: false hasContentIssue false
  • English
  • Français

The 4-Rank of K2(0)

Published online by Cambridge University Press:  20 November 2018

P. E. Conner  and
Jurgen Hurrelbrink
P. E. Conner
Affiliation:
Lousiana State University, Baton Rouge, Louisiana
Jurgen Hurrelbrink
Affiliation:
Lousiana State University, Baton Rouge, Louisiana
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let 0F) denote the integers of an algebraic number field F. Classically the Dirichlet Units Theorem gives us the structure of the K-group K1(0F). Then recently the structure of the K-group K3(0F) was found by Merkurjev and Suslin, [11]. But as of now we have only limited information about the structure of the tame kernel K2(0F).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 41 , Issue 5 , 01 October 1989 , pp. 932 - 960
Copyright
Copyright © Canadian Mathematical Society 1989

References

1. Brauckmann, B., Die 2-Sylowgruppe des zahmen Kerns total-reeller Zahlkörper, Thesis, Münster (1987).Google Scholar
2. Browkin, J.and Schinzel, A., On Sylow 2-subgroups of K2(OF) for quadratic number fields F, J. reine angew. Math 331 (1982), 104–113.Google Scholar
3. Candiotti, A.and Kramer, K., On the 2-Sylow subgroup of the Hilbert kernel of K2 of number fields, preprint (1987).Google Scholar
4. Conner, P. E. and Hurrelbrink, J., Class number parity, Series Pure Math. 8 (World Scientific Publ. Co., Singapore, 1988).Google Scholar
5. Hurrelbrink, J., Class numbers, units, and K2, to appear in Proc. Alg. K-Th. Conf. Lake Louise, Canada (1987), NATO ASI Series.Google Scholar
6. Hurrelbrink, J.and Kolster, M., On the 2-primary part of the Birch-Tate conjecture for cyclotomic fields, Contemp. Math. 55 (1986), 519–528.Google Scholar
7. Keune, F., On the structure of K2 of the ring of integers in a number field, preprint (1987).Google Scholar
8. Kolster, M., The structure of the 2-Sylow subgroup of K2(O), I, Comment. Math. Helvetici 61 (1986), 376–388.Google Scholar
9. Kolster, M., The structure of the 2-Sylow subgroup of K2(O), II, K-Theory 1 (1987), 467–479.Google Scholar
10. Lam, T. Y., The algebraic theory of quadratic forms (Reading, Mass, 1973).Google Scholar
11. Merkurjev, A. S. and Suslin, A. A., On the K3 of fields, preprint (1987).Google Scholar
12. Milnor, J., Introduction to algebraic K-theory, Annals Math. Stud. 72 (Princeton, NJ, 1971).Google Scholar
13. Tate, J., Appendix to: The Milnor ring of a global field, SLNM 342 (1973), 429–446.Google Scholar
14. Tate, J., Relations between K2 and Galois cohomology, Inventiones math. 36 (1976), 257–274.Google Scholar