On two-primary algebraic K-theory of quadratic number rings with focus on K₂
Marius Crainic ; Paul Arne Østvær
Acta Arithmetica, Tome 89 (1999), p. 223-243 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)
Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:207218 
@article{bwmeta1.element.bwnjournal-article-aav87i3p223bwm,
     author = {Marius Crainic and Paul Arne \O stv\ae r},
     title = {On two-primary algebraic K-theory of quadratic number rings with focus on K2},
     journal = {Acta Arithmetica},
     volume = {89},
     year = {1999},
     pages = {223-243},
     zbl = {0931.11052},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav87i3p223bwm}
}

Marius Crainic; Paul Arne Østvær. On two-primary algebraic K-theory of quadratic number rings with focus on K₂. Acta Arithmetica, Tome 89 (1999) pp. 223-243. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav87i3p223bwm/

[000] [1] M. C. Boldy, The 2-primary component of the tame kernel of quadratic number fields, Ph.D. thesis, Catholic University of Nijmegen, 1991.

[001] [2] A. Borel, Cohomologie réelle stable des groupes S-arithmétiques classiques, C. R. Acad. Sci. Paris 7 (1974), 235-272.

[002] [3] J. Browkin and H. Gangl, Table of tame and wild kernels of quadratic imaginary number fields of discriminants > - 5000 (conjectural values), Math. Comp., to appear. | Zbl 0919.11079

[003] [4] J. Browkin and A. Schinzel, On Sylow 2-subgroups of K₂F for quadratic number fields F, J. Reine Angew. Math. 331 (1982), 104-113. | Zbl 0493.12013

[004] [5] P. E. Conner and J. Hurrelbrink, The 4-rank of K₂(𝓞), Canad. J. Math. 41 (1989), 932-960. | Zbl 0705.19006

[005] [6] A. Fröhlich and R. Taylor, Algebraic Number Theory, Cambridge Stud. Adv. Math. 27, Cambridge Univ. Press, 1993.

[006] [7] M. Ishida, The Genus Fields of Algebraic Number Fields, Lecture Notes in Math. 555, Springer, 1976. | Zbl 0353.12001

[007] [8] F. Keune, On the structure of the K₂ of ring of integers in a number field, K-Theory 2 (1989), 625-645. | Zbl 0705.19007

[008] [9] M. Kolster, The structure of the 2-Sylow subgroup of K₂(𝓞), I, Comment. Math. Helv. 61 (1986), 376-388. | Zbl 0601.12017

[009] [10] P. Morton, On Redei's theory of the Pell equation, J. Reine Angew. Math. 307/308 (1978), 373-398. | Zbl 0395.12018

[010] [11] J. Neukirch, Class Field Theory, Grundlehren Math. Wiss. 280, Springer, 1986. | Zbl 0587.12001

[011] [12] H. Qin, The 2-Sylow subgroups of the tame kernel of imaginary quadratic fields, Acta Arith. 69 (1995), 153-169. | Zbl 0826.11055

[012] [13] H. Qin, The 4-rank of K₂OF for real quadratic fields F, Acta Arith. 72 (1995), 323-333.

[013] [14] D. Quillen, Finite Generation of the Groups Ki of Rings of Algebraic Integers, Lectures Notes in Math. 341, Springer, 1973, 179-198. | Zbl 0355.18018

[014] [15] J. Rognes and C. Weibel, Two-primary algebraic K-theory of rings of integers in number fields, preprint, 1997; http://www.math.uiuc.edu/K-theory/0220/.

[015] [16] J. Tate, Relations between K₂ and Galois cohomology, Invent. Math. 36 (1976), 257-274. | Zbl 0359.12011

[016] [17] A. Vazzana, On the 2-primary part of K₂ of rings of integers in certain quadratic number fields, Acta Arith. 80 (1997), 225-235. | Zbl 0868.11054

[017] [18] A. Vazzana, Elementary abelian 2-primary parts of K₂𝓞 and related graphs in certain quadratic number fields, Acta Arith. 81 (1997), 253-264. | Zbl 0905.11051