## 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.

Original language | English |
---|---|

Article number | e40 |

Pages (from-to) | 1-47 |

Number of pages | 47 |

Journal | Forum of Mathematics, Sigma |

Volume | 9 |

Early online date | 24 May 2021 |

DOIs | |

Publication status | Published - 2021 |

## Fingerprint

Dive into the research topics of 'Hyperbolic tessellations and generators of K_{3}for imaginary quadratic fields'. Together they form a unique fingerprint.