Abstract
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 this prediction is valid for all abelian number fields.
Publisher
Cambridge University Press (CUP)
Subject
Computational Mathematics,Discrete Mathematics and Combinatorics,Geometry and Topology,Mathematical Physics,Statistics and Probability,Algebra and Number Theory,Theoretical Computer Science,Analysis
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