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arXiv · 1310.6219

The number of varieties in a family which contain a rational point

Daniel Loughran
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Abstract

We consider the problem of counting the number of varieties in a family over a number field which contain a rational point. In particular, for products of Brauer-Severi varieties and closely related counting functions associated to Brauer group elements. Using harmonic analysis on toric varieties, we provide a positive answer to a question of Serre on such counting functions in some cases. We also formulate some conjectures on generalisations of Serre's problem.

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Daniel Loughran. 2013-10-23. The number of varieties in a family which contain a rational point. https://arxiv.org/abs/1310.6219

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