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arXiv · 1011.1430

On the Brauer-Manin obstruction for cubic surfaces

Andreas-Stephan Elsenhans·Jörg Jahnel
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Abstract

We describe a method to compute the Brauer-Manin obstruction for smooth cubic surfaces over $\bbQ$ such that $\Br(S)/\Br(\bbQ)$ is of order two or four. This covers the vast majority of the cases when this group is non-zero. Our approach is to associate a Brauer class with every Galois invariant double-six. We show that all order two Brauer classes may be obtained in this way. We also recover Sir Peter Swinnerton-Dyer's result that $\Br(S)/\Br(\bbQ)$ may take only five values.

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Andreas-Stephan Elsenhans, Jörg Jahnel. 2010-11-05. On the Brauer-Manin obstruction for cubic surfaces. https://arxiv.org/abs/1011.1430

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