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arXiv · 1711.00569

The d-primary Brauer-Manin obstruction for Curves

Brendan Creutz·Bianca Viray·José Felipe Voloch
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Abstract

For a curve over a global field we consider for which integers d the d-primary part of the Brauer group can obstruct the existence of rational points. We give examples showing it is possible that there is a d-primary obstruction for infinitely many relatively coprime d, and also an example where the odd part of the Brauer group does not obstruct although there is a Brauer-Manin obstruction. These examples demonstrate that a slightly stronger form of a conjecture of Poonen is false, despite being supported by the same heuristic.

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Brendan Creutz, Bianca Viray, José Felipe Voloch. 2017-11-02. The d-primary Brauer-Manin obstruction for Curves. https://arxiv.org/abs/1711.00569

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