David Burns
Hyperbolic tessellations and generators of for imaginary quadratic fields
Burns, David; de Jeu, Rob; Gangl, Herbert; Rahm, Alexander D.; Yasaki, Dan
Authors
Rob de Jeu
Professor Herbert Gangl herbert.gangl@durham.ac.uk
Professor
Alexander D. Rahm
Dan Yasaki
Abstract
We develop methods for constructing explicit generators, modulo torsion, of the K3 -groups of imaginary quadratic number fields. These methods are based on either tessellations of hyperbolic 3 -space or on direct calculations in suitable pre-Bloch groups and lead to the very first proven examples of explicit generators, modulo torsion, of any infinite K3 -group of a number field. As part of this approach, we make several improvements to the theory of Bloch groups for K3 of any field, predict the precise power of 2 that should occur in the Lichtenbaum conjecture at −1 and prove that this prediction is valid for all abelian number fields.
Citation
Burns, D., de Jeu, R., Gangl, H., Rahm, A. D., & Yasaki, D. (2021). Hyperbolic tessellations and generators of for imaginary quadratic fields. Forum of Mathematics, Sigma, 9, Article e40. https://doi.org/10.1017/fms.2021.9
Journal Article Type | Article |
---|---|
Online Publication Date | May 24, 2021 |
Publication Date | 2021 |
Deposit Date | May 24, 2021 |
Publicly Available Date | Nov 1, 2021 |
Journal | Forum of Mathematics, Sigma |
Print ISSN | 2050-5094 |
Publisher | Cambridge University Press |
Peer Reviewed | Peer Reviewed |
Volume | 9 |
Article Number | e40 |
DOI | https://doi.org/10.1017/fms.2021.9 |
Related Public URLs | arxiv.org/abs/1909.09091 |
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http://creativecommons.org/licenses/by-nc-nd/4.0/
Copyright Statement
This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives licence (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is unaltered and is properly cited. The written permission of Cambridge University Press must be obtained for commercial re-use or in order to create a derivative work.
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