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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Tame and wild kernels
of quadratic imaginary number fields


Authors: Jerzy Browkin and Herbert Gangl
Journal: Math. Comp. 68 (1999), 291-305
MSC (1991): Primary 11R11; Secondary 11R70, 11Y40, 19C99, 19F27
MathSciNet review: 1604336
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Abstract | References | Similar Articles | Additional Information

Abstract: For all quadratic imaginary number fields $F$ of discriminant
$d>-5000,$ we give the conjectural value of the order of Milnor's group (the tame kernel) $K_{2}O_{F},$ where $O_{F}$ is the ring of integers of $F.$ Assuming that the order is correct, we determine the structure of the group $K_{2}O_{F}$ and of its subgroup $W_{F}$ (the wild kernel). It turns out that the odd part of the tame kernel is cyclic (with one exception, $d=-3387$).


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Additional Information

Jerzy Browkin
Affiliation: Jerzy Browkin, Institute of Mathematics, University of Warsaw, ul. Banacha 2, PL-02-097 Warszawa, Poland
Email: bro@mimuw.edu.pl

Herbert Gangl
Affiliation: Herbert Gangl, Institute for Experimental Mathematics, Ellernstr. 29, D-45326 Essen, Germany
Email: herbert@mpim-bonn.mpg.de

DOI: http://dx.doi.org/10.1090/S0025-5718-99-01000-5
PII: S 0025-5718(99)01000-5
Keywords: Tame kernel, wild kernel, quadratic imaginary fields, Lichtenbaum's conjecture
Received by editor(s): January 3, 1997
Additional Notes: The second author was supported by the Deutsche Forschungsgemeinschaft.
Article copyright: © Copyright 1999 American Mathematical Society