The 4-Rank of K 2(0)
Canadian journal of mathematics, Tome 41 (1989) no. 5, pp. 932-960

Voir la notice de l'article provenant de la source Cambridge University Press

Let 0 F) denote the integers of an algebraic number field F. Classically the Dirichlet Units Theorem gives us the structure of the K-group K1(0 F). Then recently the structure of the K-group K3(0 F) was found by Merkurjev and Suslin, [11]. But as of now we have only limited information about the structure of the tame kernel K2(0 F).
Conner, P. E.; Hurrelbrink, Jurgen. The 4-Rank of K 2(0). Canadian journal of mathematics, Tome 41 (1989) no. 5, pp. 932-960. doi: 10.4153/CJM-1989-043-0
@article{10_4153_CJM_1989_043_0,
     author = {Conner, P. E. and Hurrelbrink, Jurgen},
     title = {The {4-Rank} of {K} 2(0)},
     journal = {Canadian journal of mathematics},
     pages = {932--960},
     year = {1989},
     volume = {41},
     number = {5},
     doi = {10.4153/CJM-1989-043-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1989-043-0/}
}
TY  - JOUR
AU  - Conner, P. E.
AU  - Hurrelbrink, Jurgen
TI  - The 4-Rank of K 2(0)
JO  - Canadian journal of mathematics
PY  - 1989
SP  - 932
EP  - 960
VL  - 41
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1989-043-0/
DO  - 10.4153/CJM-1989-043-0
ID  - 10_4153_CJM_1989_043_0
ER  - 
%0 Journal Article
%A Conner, P. E.
%A Hurrelbrink, Jurgen
%T The 4-Rank of K 2(0)
%J Canadian journal of mathematics
%D 1989
%P 932-960
%V 41
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1989-043-0/
%R 10.4153/CJM-1989-043-0
%F 10_4153_CJM_1989_043_0

[1] 1. Brauckmann, B., Die 2-Sylowgruppe des zahmen Kerns total-reeller Zahlkörper, Thesis, Münster (1987). Google Scholar

[2] 2. Browkin, J.and Schinzel, A., On Sylow 2-subgroups of K2(O) for quadratic number fields F, J. reine angew. Math 331 (1982), 104–113. Google Scholar

[3] 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] 4. Conner, P. E. and Hurrelbrink, J., Class number parity, Series Pure Math. 8 (World Scientific Publ. Co., Singapore, 1988). Google Scholar

[5] 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] 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] 7. Keune, F., On the structure of K2 of the ring of integers in a number field, preprint (1987). Google Scholar

[8] 8. Kolster, M., The structure of the 2-Sylow subgroup of K2(O), I, Comment. Math. Helvetici 61 (1986), 376–388. Google Scholar

[9] 9. Kolster, M., The structure of the 2-Sylow subgroup of K2(O), II, K-Theory 1 (1987), 467–479. Google Scholar

[10] 10. Lam, T. Y., The algebraic theory of quadratic forms (Reading, Mass, 1973). Google Scholar

[11] 11. Merkurjev, A. S. and Suslin, A. A., On the K of fields, preprint (1987). Google Scholar

[12] 12. Milnor, J., Introduction to algebraic K-theory, Annals Math. Stud. 72 (Princeton, NJ, 1971). Google Scholar

[13] 13. Tate, J., Appendix to: The Milnor ring of a global field, SLNM 342 (1973), 429–446. Google Scholar

[14] 14. Tate, J., Relations between K2 and Galois cohomology, Inventiones math. 36 (1976), 257–274. Google Scholar

Cité par Sources :