tame kernel
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2016 ◽  
Vol 158 ◽  
pp. 244-267 ◽  
Author(s):  
Chaochao Sun ◽  
Kejian Xu
Keyword(s):  


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


2014 ◽  
Vol 42 (7) ◽  
pp. 2779-2787
Author(s):  
Xia Wu ◽  
Zhengjun Zhao
Keyword(s):  


Author(s):  
Jerzy Browkin ◽  
Herbert Gangl

AbstractAssuming a version of the Lichtenbaum conjecture, we apply Brauer-Kuroda relations between the Dedekind zeta function of a number field and the zeta function of some of its subfields to prove formulas relating the order of the tame kernel of a number field F with the orders of the tame kernels of some of its subfields. The details are given for fields F which are Galois over ℚ with Galois group the group ℤ/2 × ℤ/2, the dihedral group D2p; p an odd prime, or the alternating group A4. We include numerical results illustrating these formulas.



2009 ◽  
Vol 05 (03) ◽  
pp. 383-405
Author(s):  
JONATHAN W. SANDS

Fix a Galois extension [Formula: see text] of totally real number fields such that the Galois group G has exponent 2. Let S be a finite set of primes of F containing the infinite primes and all those which ramify in [Formula: see text], let [Formula: see text] denote the primes of [Formula: see text] lying above those in S, and let [Formula: see text] denote the ring of [Formula: see text]-integers of [Formula: see text]. We then compare the Fitting ideal of [Formula: see text] as a ℤ[G]-module with a higher Stickelberger ideal. The two extend to the same ideal in the maximal order of ℚ[G], and hence in ℤ[1/2][G]. Results in ℤ[G] are obtained under the assumption of the Birch–Tate conjecture, especially for biquadratic extensions, where we compute the index of the higher Stickelberger ideal. We find a sufficient condition for the Fitting ideal to contain the higher Stickelberger ideal in the case where [Formula: see text] is a biquadratic extension of F containing the first layer of the cyclotomic ℤ2-extension of F, and describe a class of biquadratic extensions of F = ℚ that satisfy this condition.



2009 ◽  
Vol 37 (2) ◽  
pp. 630-638 ◽  
Author(s):  
Haiyan Zhou
Keyword(s):  






2007 ◽  
Vol 209 (1) ◽  
pp. 245-253 ◽  
Author(s):  
Hourong Qin ◽  
Haiyan Zhou


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