Geodesic
Hyperbolic tessellations and generators of ${K}_{\textbf {3}}$ for imaginary quadratic fields
Forum of Mathematics, Sigma, Tome 9 (2021)

Voir la notice de l'article provenant de la source Cambridge University Press

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 this prediction is valid for all abelian number fields. 
@article{10_1017_fms_2021_9,
     author = {David Burns and Rob de Jeu and Herbert Gangl and Alexander D. Rahm and Dan Yasaki},
     title = {Hyperbolic tessellations and generators of ${K}_{\textbf {3}}$ for imaginary quadratic fields},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {9},
     year = {2021},
     doi = {10.1017/fms.2021.9},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2021.9/}
}
TY  - JOUR
AU  - David Burns
AU  - Rob de Jeu
AU  - Herbert Gangl
AU  - Alexander D. Rahm
AU  - Dan Yasaki
TI  - Hyperbolic tessellations and generators of ${K}_{\textbf {3}}$ for imaginary quadratic fields
JO  - Forum of Mathematics, Sigma
PY  - 2021
VL  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1017/fms.2021.9/
DO  - 10.1017/fms.2021.9
LA  - en
ID  - 10_1017_fms_2021_9
ER  - 
%0 Journal Article
%A David Burns
%A Rob de Jeu
%A Herbert Gangl
%A Alexander D. Rahm
%A Dan Yasaki
%T Hyperbolic tessellations and generators of ${K}_{\textbf {3}}$ for imaginary quadratic fields
%J Forum of Mathematics, Sigma
%D 2021
%V 9
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1017/fms.2021.9/
%R 10.1017/fms.2021.9
%G en
%F 10_1017_fms_2021_9
David Burns; Rob de Jeu; Herbert Gangl; Alexander D. Rahm; Dan Yasaki. Hyperbolic tessellations and generators of ${K}_{\textbf {3}}$ for imaginary quadratic fields. Forum of Mathematics, Sigma, Tome 9 (2021). doi: 10.1017/fms.2021.9

Cité par Sources :