On the order three Brauer classes for cubic surfaces

Abstract

We describe a method to compute the Brauer-Manin obstruction for smooth cubic surfaces over $\mathbb{Q}$ such that $\Br(S)/\Br(\bbQ)$ is a 3-group. Our approach is to associate a Brauer class with every ordered triplet of Galois invariant pairs of Steiner trihedra. We show that all order three Brauer classes may be obtained in this way. To show the effect of the obstruction, we give explicit examples.

Extended introduction, discussion of the example of Cassels and Guy

References in corpus (1)

• On the Brauer-Manin obstruction for cubic surfaces