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Remarks on the $ K_2 $ group of $ \mathbb{Z}[\zeta_p] $

  • Received: 15 July 2021 Revised: 14 December 2021 Accepted: 27 December 2021 Published: 12 January 2022
  • MSC : 19C99, 19F15

  • In this paper, our aim is to obtain the $ K_2 $ analogues of both the Herbrand-Ribet theorem and the Vandiver's conjecture.

    Citation: Daochang Zhang, Chaochao Sun. Remarks on the $ K_2 $ group of $ \mathbb{Z}[\zeta_p] $[J]. AIMS Mathematics, 2022, 7(4): 5920-5924. doi: 10.3934/math.2022329

    Related Papers:

  • In this paper, our aim is to obtain the $ K_2 $ analogues of both the Herbrand-Ribet theorem and the Vandiver's conjecture.



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    [7] K. A. Ribet, A modular construction of unramified $p$-extensions of $\mathbb{Q}(\zeta_p)$, Invent. Math., 34 (1976), 151–162. https://doi.org/10.1007/BF01403065 doi: 10.1007/BF01403065
    [8] L. Taelman, A Herbrand-Ribet theorem for function fields, Invent. Math., 188 (2012), 253–275. https://doi.org/10.1007/s00222-011-0346-3 doi: 10.1007/s00222-011-0346-3
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  • © 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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