Daniel Loughran
Published 2013-10-23, updated 2014-11-20Version 2
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.
Comments: 42 pages. Improved the formatting and the conjectural framework
A new conjecture on rational points in families
Rational points in a family of conics over $\mathbb{F}_2(t)$
Serre's problem on the density of isotropic fibres in conic bundles
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