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On generators of the Chow group of 0-cycles on diagonal cubic surfaces over 3-adic fields

Volume 181 / 2017

Kento Yamamoto Acta Arithmetica 181 (2017), 75-84 MSC: Primary 14C15, 14J26; Secondary 11G25. DOI: 10.4064/aa8646-5-2017 Published online: 30 October 2017

Abstract

We show that the degree-zero part of the Chow group of $0$-cycles on some diagonal cubic surface over a 3-adic field is generated by the classes of rational points. In the proof of the main result, we will construct explicit generators over the cubic unramified scalar extension. A key point is to check that such cycles have non-zero values under the Brauer–Manin pairing. We will use the Hilbert symbol to compute them.

Authors

  • Kento YamamotoDepartment of Mathematics
    Chuo University
    1-13-27 Kasuga, Bunkyo-Ku
    Tokyo 112-8551, Japan
    e-mail

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