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arXiv · 1909.09091

Hyperbolic tessellations and generators of K_3 for imaginary quadratic fields

David Burns·Rob de Jeu·Herbert Gangl·Alexander D. Rham·Dan Yasaki
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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.

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David Burns, Rob de Jeu, Herbert Gangl, Alexander D. Rham, Dan Yasaki. 2019-09-19. Hyperbolic tessellations and generators of K_3 for imaginary quadratic fields. https://doi.org/10.1017/fms.2021.9

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