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

• Autorzy: Marius Crainic , Paul Arne Østvær
• Języki publikacji: EN

Słowa kluczowe

EN

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

Kategorie tematyczne

• 14F20: \'Etale and other Grothendieck topologies and (co)homologies
• 11R11: Quadratic extensions
• 11R65: Class groups and Picard groups of orders
• 19D50: Computations of higher K -theory of rings
• 19C99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1998-1999
• Tom: 87
• Numer: 3
• Strony: 223-243

Daty

wydano

1999

otrzymano

1997-10-21

poprawiono

1998-02-27

Twórcy

autor

Marius Crainic

• Department of Mathematics, University of Utrecht, Utrecht, The Netherlands

autor

Paul Arne Østvær

• Department of Mathematics, University of Oslo, Oslo, Norway

Bibliografia

• [1] M. C. Boldy, The 2-primary component of the tame kernel of quadratic number fields, Ph.D. thesis, Catholic University of Nijmegen, 1991.
• [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 $K₂𝓞_F$ 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(𝓞), 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(𝓞), 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 $K₂O_F$ for real quadratic fields F, Acta Arith. 72 (1995), 323-333.
• [14] D. Quillen, Finite Generation of the Groups $K_i$ 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 K₂𝓞 and related graphs in certain quadratic number fields, Acta Arith. 81 (1997), 253-264.