Hyperbolic tessellations and generators of K_3 for imaginary quadratic fields
Abstract
We develop methods for constructing explicit generators, modulo torsion, of the K_3-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 K_3-group of a number field. As part of this approach, we make several improvements to the theory of Bloch groups for K_3 of any field, predict the precise power of 2 that should occur in the Lichtenbaum conjecture at -1 and prove that the latter prediction is valid for all abelian number fields.
Keywords
Cite
@article{arxiv.1909.09091,
title = {Hyperbolic tessellations and generators of K_3 for imaginary quadratic fields},
author = {David Burns and Rob de Jeu and Herbert Gangl and Alexander D. Rham and Dan Yasaki},
journal= {arXiv preprint arXiv:1909.09091},
year = {2021}
}
Comments
51 pages; in this revision, the exposition and a few proofs were shortened, and a brief comparison with earlier work added