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Hyperbolic tessellations and generators of K_3 for imaginary quadratic fields

Abstract : We develop methods for constructing explicit generating elements, 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 infinite 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.
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Submitted on : Tuesday, April 21, 2020 - 11:03:01 PM
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INSMI | UPF | 35430 | ANR

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David Burns, Rob M. H. de Jeu, Herbert Gangl, Alexander D. Rahm, Dan yasaki. Hyperbolic tessellations and generators of K_3 for imaginary quadratic fields. Forum of Mathematics, Sigma, Cambridge University press, 2021, 9 (E40), ⟨10.1017/fms.2021.9⟩. ⟨hal-02550079⟩

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