The 8-rank of tame kernels of quadratic number fields

2012 ◽  
Vol 152 (4) ◽  
pp. 407-424 ◽  
Author(s):  
Xuejun Guo ◽  
Hourong Qin
Keyword(s):  
Number Fields ◽  
Quadratic Number ◽  
Quadratic Number Fields ◽  
Tame Kernels

The Structure of the Tame Kernels of Quadratic Number Fields (III)

2008 ◽  
Vol 36 (3) ◽  
pp. 1012-1033 ◽  
Author(s):  
Xiaobin Yin ◽  
Hourong Qin ◽  
Qunsheng Zhu
Keyword(s):  
Number Fields ◽  
Quadratic Number ◽  
Quadratic Number Fields ◽  
Tame Kernels

scholarly journals The structure of the tame kernels of quadratic number fields (II)

2005 ◽  
Vol 116 (3) ◽  
pp. 217-262 ◽  
Author(s):  
Xiaobin Yin ◽  
Hourong Qin ◽  
Qunsheng Zhu
Keyword(s):  
Number Fields ◽  
Quadratic Number ◽  
Quadratic Number Fields ◽  
Tame Kernels

scholarly journals Hyperbolic tessellations and generators of for imaginary quadratic fields

2021 ◽  
Vol 9 ◽  
Author(s):  
David Burns ◽  
Rob de Jeu ◽  
Herbert Gangl ◽  
Alexander D. Rahm ◽  
Dan Yasaki
Keyword(s):  
Number Field ◽  
Number Fields ◽  
Quadratic Fields ◽  
Quadratic Number ◽  
Imaginary Quadratic Fields ◽  
Quadratic Number Fields ◽  
Formula Group ◽  
Imaginary Quadratic Number ◽  
Direct Calculations

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.

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