On the Brauer group of diagonal cubic surfaces
Algebraic Geometry
2014-12-02 v1 Number Theory
Abstract
We are concerned with finding explicit generators of the Brauer group of diagonal cubic surfaces in terms of norm residue symbols, which was originally studied by Manin. We introduce the notion of uniform generators and find that the Brauer group of some classes of diagonal cubic surfaces have uniform generators. However, we also prove that the Brauer group of general diagonal cubic surfaces do not have such ones. This reveals that a result of Manin for certain diagonal cubic surfaces cannot be generalized in some sense.
Cite
@article{arxiv.1412.0087,
title = {On the Brauer group of diagonal cubic surfaces},
author = {Tetsuya Uematsu},
journal= {arXiv preprint arXiv:1412.0087},
year = {2014}
}
Comments
21 pages