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Tame kernels of pure cubic fields

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Abstract

In this paper, we study the p-rank of the tame kernels of pure cubic fields. In particular, we prove that for a fixed positive integer m, there exist infinitely many pure cubic fields whose 3-rank of the tame kernel equal to m. As an application, we determine the 3-rank of their tame kernels for some special pure cubic fields.

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Authors and Affiliations

  1. School of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, P. R. China

    Xiao Yun Cheng

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  1. Xiao Yun Cheng
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Correspondence to Xiao Yun Cheng.

Additional information

Supported by National Natural Science Foundation of China (Grant Nos. 10971091 and 10871088), Specialized Research Fund for the Doctoral Program of Higher Education (Grant Nos. 200802840003 and 200802841042)

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Cheng, X.Y. Tame kernels of pure cubic fields. Acta. Math. Sin.-English Ser. 28, 771–780 (2012). https://doi.org/10.1007/s10114-011-0089-5

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  • DOI: https://doi.org/10.1007/s10114-011-0089-5

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