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ArticleOriginal scientific text

Title

On two-primary algebraic K-theory of quadratic number rings with focus on K₂

Authors 1, 2

Affiliations

  1. Department of Mathematics, University of Utrecht, Utrecht, The Netherlands
  2. Department of Mathematics, University of Oslo, Oslo, Norway

Keywords

ENG
algebraic K-groups of quadratic number rings, 2- and 4-rank formulas for Picard groups, étale cohomology

Bibliography

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  2. A. Borel, Cohomologie réelle stable des groupes S-arithmétiques classiques, C. R. Acad. Sci. Paris 7 (1974), 235-272.
  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.
  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.
  5. P. E. Conner and J. Hurrelbrink, The 4-rank of K₂(), Canad. J. Math. 41 (1989), 932-960.
  6. A. Fröhlich and R. Taylor, Algebraic Number Theory, Cambridge Stud. Adv. Math. 27, Cambridge Univ. Press, 1993.
  7. M. Ishida, The Genus Fields of Algebraic Number Fields, Lecture Notes in Math. 555, Springer, 1976.
  8. F. Keune, On the structure of the K₂ of ring of integers in a number field, K-Theory 2 (1989), 625-645.
  9. M. Kolster, The structure of the 2-Sylow subgroup of K₂(), I, Comment. Math. Helv. 61 (1986), 376-388.
  10. P. Morton, On Redei's theory of the Pell equation, J. Reine Angew. Math. 307/308 (1978), 373-398.
  11. J. Neukirch, Class Field Theory, Grundlehren Math. Wiss. 280, Springer, 1986.
  12. H. Qin, The 2-Sylow subgroups of the tame kernel of imaginary quadratic fields, Acta Arith. 69 (1995), 153-169.
  13. H. Qin, The 4-rank of K₂OF for real quadratic fields F, Acta Arith. 72 (1995), 323-333.
  14. D. Quillen, Finite Generation of the Groups Ki of Rings of Algebraic Integers, Lectures Notes in Math. 341, Springer, 1973, 179-198.
  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/.
  16. J. Tate, Relations between K₂ and Galois cohomology, Invent. Math. 36 (1976), 257-274.
  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.
  18. A. Vazzana, Elementary abelian 2-primary parts of K₂ and related graphs in certain quadratic number fields, Acta Arith. 81 (1997), 253-264.
Acta Arithmetica
1998-1999/87/3
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Pages:
223-243
Main language of publication
English
Received
1997-10-21
Accepted
1998-02-27
Published
1999
Exact and natural sciences