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Bi-Quadratic Number Fields with Trivial 2-Primary Hilbert Kernels

Published online by Cambridge University Press:  25 June 2003

Manfred Kolster  and
Abbas Movahhedi
Manfred Kolster
Affiliation:
Department of Mathematics, McMaster University, 1280 Main Street West, Hamilton, Ontario L8S 4K1, Canada. E-mail: [email protected]
Abbas Movahhedi
Affiliation:
LACO (UMR 6090 CNRS), Faculté des Sciences et Techniques, 123 Avenue Albert Thomas, 87060 Limoges Cedex, France. E-mail: [email protected]
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Abstract

Using results of Browkin and Schinzel one can easily determine quadratic number fields with trivial 2-primary Hilbert kernels. In the present paper we completely determine all bi-quadratic number fields which have trivial 2-primary Hilbert kernels. To obtain our results, we use several different tools, amongst which is the genus formula for the Hilbert kernel of an arbitrary relative quadratic extension, which is of independent interest. For some cases of real bi-quadratic fields there is an ambiguity in the genus formula, so in this situation we use instead Brauer relations between the Dedekind zeta-funtions and the Birch–Tate conjecture.

Keywords

K-theoryHilbert kernelbi-quadratic fields11R7019F15
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 87 , Issue 1 , July 2003 , pp. 109 - 136
Copyright
2003 London Mathematical Society

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Footnotes

The research of the first author was partially supported by NSERC grant #OGP 0042510.