@article{5226aad4ae054da4a4e8327dc359b30d,
title = "Hyperbolic tessellations and generators of K3 for imaginary quadratic fields",
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.",
author = "David Burns and {de Jeu}, Rob and Herbert Gangl and Rahm, {Alexander D.} and Dan Yasaki",
note = "Publisher Copyright: {\textcopyright} The Author(s), 2021. Published by Cambridge University Press. 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. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",
year = "2021",
month = may,
day = "24",
doi = "10.1017/fms.2021.9",
language = "English",
volume = "9",
pages = "1--47",
journal = "Forum of Mathematics, Sigma",
issn = "2050-5094",
publisher = "Cambridge University Press",
}