Hyperbolic tessellations and generators of K3 for imaginary quadratic fields

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

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
89 Downloads (Pure)

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 statusE-pub ahead of print - 24 May 2021

Fingerprint

Dive into the research topics of 'Hyperbolic tessellations and generators of K3 for imaginary quadratic fields'. Together they form a unique fingerprint.

Cite this