Hyperbolic tessellations and generators of K 3 for imaginary quadratic fields

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

Research output: Contribution to JournalArticleAcademicpeer-review

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.
Original languageEnglish
Article numbere40
Pages (from-to)1-47
Number of pages47
JournalForum of Mathematics, Sigma
Volume9
Early online date24 May 2021
DOIs
Publication statusPublished - 2021

Funding

We thank Philippe Elbaz-Vincent for useful conversations and Nguyen Quang Do for helpful comments. We are grateful to the Irish Research Council for funding a work stay of the fourth author in Amsterdam and to the De Brun Centre for Computational Homological Algebra for funding a work stay of the second author in Galway. We also thank Mathematisches Forschungsinstitut Oberwolfach for hosting the last four authors as part of their Research in Pairs program for this project. The fifth author was partially supported by NSA grant H98230-15-1-0228. This article is submitted for publication with the understanding that the United States government is authorised to produce and distribute reprints.

FundersFunder number
National Security AgencyH98230-15-1-0228
Irish Research Council

    Fingerprint

    Dive into the research topics of 'Hyperbolic tessellations and generators of K 3 for imaginary quadratic fields'. Together they form a unique fingerprint.

    Cite this