2019/09/30 by David Burns, Rob de Jeu, Herbert Gangl +3
Mathematics · #Abelian group #Algebra over a field #Algebraic and Geometric Analysis #Binary quadratic form #Conjecture #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Modulo #Quadratic equation #Quadratic field #The Imaginary #math.KT #math.NT #msc:11G55 #msc:11R42 #msc:11R70 #msc:19D45 #msc:19F27 #msc:20H20 #msc:51M20
paper · pdf · doi:10.1017/fms.2021.9
published as Forum of Mathematics, Sigma, volume 9 (2021) · 51 pages; in this revision, the exposition and a few proofs were shortened, and a brief comparison with earlier work added
openalex created_date 2019/09/26 · arxiv created 2020/11/25 · openalex publication_date 2021/01/01 · arxiv updated 2021/05/25 · openalex updated_date 2026/08/05
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.