Symbolic generators of the Brauer group of diagonal cubic surfaces and their applications to zero-cycles (Algebraic Number Theory and Related Topics 2012)

Abstract

In this article, we first announce the result of the paper [10], in which we introduce the notion of uniform generators of the Brauer group of varieties, and consider the problem whether the Brauer group of diagonal cubic surfaces has such generators or not. The reader may refer to the paper [10] for proofs and details. Secondly, as an application of such symbolic generators, we give an example of explicit calculations of the degree-zero part of the Chow group of zero-cycles on diagonal cubic surfaces over p-adic fields, along the same line as in [9].