Geodesic
The number of varieties in a family which contain a rational point
Journal of the European Mathematical Society, Tome 20 (2018) no. 10, pp. 2539-2588.

Voir la notice de l'article provenant de la source EMS Press

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.
DOI : 10.4171/jems/818
Classification : 11-XX, 14-XX
Keywords: Rational points, families of varieties, Brauer groups, toric varieties 
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     author = {Daniel Loughran},
     title = {The number of varieties in a family which contain a rational point},
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Daniel Loughran. The number of varieties in a family which contain a rational point. Journal of the European Mathematical Society, Tome 20 (2018) no. 10, pp. 2539-2588. doi : 10.4171/jems/818. http://geodesic.mathdoc.fr/articles/10.4171/jems/818/

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