Tame kernels and second regulators of number fields and their subfields

Browkin, Jerzy; Gangl, Herbert

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 D 2p, p an odd prime, or the alternating group A4. We include numerical results illustrating these formulas. © 2013 ISOPP.

Citation

Browkin, J., & Gangl, H. (2013). Tame kernels and second regulators of number fields and their subfields. K-Theory, 12(1), 137-165. https://doi.org/10.1017/is013005031jkt229

• Journal Article Type: Article
• Online Publication Date: Jul 17, 2013
• Publication Date: Aug 1, 2013
• Deposit Date: Mar 6, 2025
• Journal: Journal of K-Theory
• Print ISSN: 0920-3036
• Electronic ISSN: 1573-0514
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 12
• Issue: 1
• Pages: 137-165
• DOI: https://doi.org/10.1017/is013005031jkt229
• Public URL: https://durham-repository.worktribe.com/output/3681359