The tame kernel of $\mathbb {Q}(\zeta _{5})$ is trivial

2015 ◽  
Vol 85 (299) ◽  
pp. 1523-1538 ◽  
Author(s):  
Long Zhang ◽  
Kejian Xu
Keyword(s):  
Tame Kernel

Values at s = −1 of L -functions for multi-quadratic extensions of number fields and annihilation of the tame kernel

2007 ◽  
Vol 76 (3) ◽  
pp. 545-555 ◽  
Author(s):  
Jonathan W. Sands ◽  
Lloyd D. Simons
Keyword(s):  
Number Fields ◽  
Quadratic Extensions ◽  
Tame Kernel

scholarly journals On the p-rank of tame kernel of number fields

2016 ◽  
Vol 158 ◽  
pp. 244-267 ◽  
Author(s):  
Chaochao Sun ◽  
Kejian Xu
Keyword(s):  
Number Fields ◽  
Tame Kernel

scholarly journals The 2-Sylow subgroups of the tame kernel of imaginary quadratic fields

1995 ◽  
Vol 69 (2) ◽  
pp. 153-169 ◽  
Author(s):  
Hourong Qin
Keyword(s):  
Quadratic Fields ◽  
Imaginary Quadratic Fields ◽  
Sylow Subgroups ◽  
Tame Kernel

scholarly journals Dyadic ideal, class group, and tame kernel in quadratic fields

2002 ◽  
Vol 166 (1-2) ◽  
pp. 229-238 ◽  
Author(s):  
Qin Yue
Keyword(s):  
Class Group ◽  
Quadratic Fields ◽  
Ideal Class ◽  
Ideal Class Group ◽  
Tame Kernel

scholarly journals L-values and the Fitting ideal of the tame kernel for relative quadratic extensions

2008 ◽  
Vol 131 (4) ◽  
pp. 389-402 ◽  
Author(s):  
Jonathan W. Sands
Keyword(s):  
Quadratic Extensions ◽  
Fitting Ideal ◽  
Tame Kernel ◽  
Relative Quadratic Extensions

scholarly journals The 4-rank of the tame kernel versus the 4-rank of the narrow class group in quadratic number fields

2000 ◽  
Vol 96 (2) ◽  
pp. 155-165 ◽  
Author(s):  
Qin Yue ◽  
Keqin Feng
Keyword(s):  
Class Group ◽  
Number Fields ◽  
Quadratic Number ◽  
Quadratic Number Fields ◽  
Tame Kernel ◽  
Narrow Class

The 4-Rank of K2(0)

1989 ◽  
Vol 41 (5) ◽  
pp. 932-960 ◽  
Author(s):  
P. E. Conner ◽  
Jurgen Hurrelbrink
Keyword(s):  
Number Field ◽  
Algebraic Number ◽  
Algebraic Number Field ◽  
Limited Information ◽  
Tame Kernel

Let 0F) denote the integers of an algebraic number field F. Classically the Dirichlet Units Theorem gives us the structure of the K-group K1(0F). Then recently the structure of the K-group K3(0F) was found by Merkurjev and Suslin, [11]. But as of now we have only limited information about the structure of the tame kernel K2(0F).

The 2-Sylow-Subgroup of the Tame Kernel of Number Fields

1991 ◽  
Vol 43 (2) ◽  
pp. 255-264 ◽  
Author(s):  
Boris Brauckmann
Keyword(s):  
Number Field ◽  
Sylow Subgroup ◽  
Class Group ◽  
Quadratic Extension ◽  
Number Fields ◽  
Surjective Homomorphism ◽  
Ring Of Integers ◽  
Tame Kernel

For a number field F with ring of integers OF the tame symbols yield a surjective homomorphism with a finite kernel, which is called the tame kernel, isomorphic to K2(OF). For the relative quadratic extension E/F, where and E ≠ F, let CS(E/ F)(2) denote the 2-Sylow-subgroup of the relative S-class-group of E over F, where S consists of all infinite and dyadic primes of F, and let m be the number of dyadic primes of F, which decompose in E.

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