On generators of the Chow group of 0-cycles on diagonal cubic surfaces over 3-adic fields
Volume 181 / 2017
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.
