Computing the tame kernel of quadratic imaginary fields
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- by Jerzy Browkin, with an appendix by Karim Belabas and Herbert Gangl;
- Math. Comp. 69 (2000), 1667-1683
- DOI: https://doi.org/10.1090/S0025-5718-00-01182-0
- Published electronically: March 15, 2000
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Abstract:
J. Tate has determined the group $K_{2}\mathcal {O}_{F}$ (called the tame kernel) for six quadratic imaginary number fields $F=\mathbb {Q}(\sqrt {d}),$ where $d=-3,-4,-7, -8,-11,$ $-15.$ Modifying the method of Tate, H. Qin has done the same for $d=-24$ and $d=-35,$ and M. Skałba for $d=-19$ and $d=-20.$ In the present paper we discuss the methods of Qin and Skałba, and we apply our results to the field $\mathbb {Q}(\sqrt {-23}).$ In the Appendix at the end of the paper K. Belabas and H. Gangl present the results of their computation of $K_{2}\mathcal {O}_{F}$ for some other values of $d.$ The results agree with the conjectural structure of $K_{2}\mathcal {O}_{F}$ given in the paper by Browkin and Gangl.References
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Bibliographic Information
- Jerzy Browkin
- Affiliation: Institute of Mathematics, University of Warsaw, ul. Banacha 2, PL-02-097 Warsaw, Poland
- Email: bro@mimuw.edu.pl
- with an appendix by Karim Belabas
- Affiliation: Dept. de Mathématiques, Bât. 425, Université Paris-Sud, F-91405 Orsay, France
- Email: Karim.Belabas@math.u-psud.fr
- Herbert Gangl
- Affiliation: Max-Planck Institut für Mathematik, Vivatsgaße 7, D-53111, Bonn, Germany
- Email: herbert@mpim-bonn.mpg.de
- Received by editor(s): January 14, 1998
- Received by editor(s) in revised form: December 7, 1998
- Published electronically: March 15, 2000
- © Copyright 2000 American Mathematical Society
- Journal: Math. Comp. 69 (2000), 1667-1683
- MSC (1991): Primary 19C20; Secondary 11R11, 11R70, 11Y40
- DOI: https://doi.org/10.1090/S0025-5718-00-01182-0
- MathSciNet review: 1681124