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$ K_2$ of certain families of plane quartic curves


Authors: Hang Liu and Shan Chang
Journal: Proc. Amer. Math. Soc. 146 (2018), 2785-2796
MSC (2010): Primary 19F27
DOI: https://doi.org/10.1090/proc/13963
Published electronically: February 8, 2018
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Abstract: We construct three elements in the kernel of the tame symbol on families of quartic curves. We show that these elements are integral under certain conditions on the parameters. Moreover, we prove that these elements are in general linearly independent by calculating the limit of the regulator.


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Additional Information

Hang Liu
Affiliation: School of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, People’s Republic of China
Email: liuhang@snnu.edu.cn

Shan Chang
Affiliation: School of Mathematics, Hefei University of Technology, Hefei 230009, People’s Republic of China
Email: changshan@hfut.edu.cn

DOI: https://doi.org/10.1090/proc/13963
Keywords: $K_2$, Beilinson's conjecture, quartic curve
Received by editor(s): June 14, 2017
Received by editor(s) in revised form: September 17, 2017, September 20, 2017, and September 22, 2017
Published electronically: February 8, 2018
Additional Notes: The second author is the coresponding author
Communicated by: Lev Borisov
Article copyright: © Copyright 2018 American Mathematical Society

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