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


Authors: Long Zhang and Kejian Xu
Journal: Math. Comp. 85 (2016), 1523-1538
MSC (2010): Primary 19C99, 19F15
DOI: https://doi.org/10.1090/mcom/3003
Published electronically: August 11, 2015
MathSciNet review: 3454374
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Abstract: In this paper, we prove that the tame kernel of the cyclotomic field $ \mathbb{Q}(\zeta _5)$ is trivial, which confirms a conjecture of Browkin.


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Additional Information

Long Zhang
Affiliation: School of Mathematics, Jilin University, Changchun, China 130012 – and – College of Mathematics, Qingdao University, Qingdao, China 266071
Email: zhanglong_note@hotmail.com

Kejian Xu
Affiliation: College of Mathematics, Qingdao University, Qingdao, China 266071
Email: kejianxu@amss.ac.cn

DOI: https://doi.org/10.1090/mcom/3003
Keywords: Number field, cyclotomic field, tame kernel, $K_2$ group
Received by editor(s): September 4, 2014
Received by editor(s) in revised form: October 9, 2014, and October 21, 2014
Published electronically: August 11, 2015
Additional Notes: This research was supported by National Natural Science Foundation of China (No. 10871106).
Article copyright: © Copyright 2015 American Mathematical Society