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Tame kernels and second regulators of number fields and their subfields

Published online by Cambridge University Press:  17 July 2013

Jerzy Browkin  and
Herbert Gangl
Jerzy Browkin
Affiliation:
Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, PL-00-956 Warsaw, Polandbrowkin@impan.pl
Herbert Gangl
Affiliation:
Department of Mathematical Sciences, South Road, University of Durham, Durham, DH1 3LE, United Kingdomherbert.gangl@durham.ac.uk
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Abstract

Assuming a version of the Lichtenbaum conjecture, we apply Brauer-Kuroda relations between the Dedekind zeta function of a number field and the zeta function of some of its subfields to prove formulas relating the order of the tame kernel of a number field F with the orders of the tame kernels of some of its subfields. The details are given for fields F which are Galois over ℚ with Galois group the group ℤ/2 × ℤ/2, the dihedral group D2p; p an odd prime, or the alternating group A4. We include numerical results illustrating these formulas.

Keywords

Dedekind zeta functionsBloch-Wigner dilogarithmBloch groupsecond regulatorBrauer-Kuroda relations11R4211G55

Information

Type
Research Article
Information
Journal of K-Theory , Volume 12 , Issue 1: Nanjing Special Issue on K-theory, number theory and geometry , August 2013 , pp. 137 - 165
Copyright
Copyright © ISOPP 2013 

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