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Hyperbolic tessellations and generators of for imaginary quadratic fields

Burns, David; de Jeu, Rob; Gangl, Herbert; Rahm, Alexander D.; Yasaki, Dan

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Authors

David Burns

Rob de Jeu

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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Publisher Licence URL
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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