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 Cet article a éte moissonné depuis la source EMS Press

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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 
@article{JEMS_2018_20_10_a5,
     author = {Daniel Loughran},
     title = {The number of varieties in a family which contain a rational point},
     journal = {Journal of the European Mathematical Society},
     pages = {2539--2588},
     year = {2018},
     volume = {20},
     number = {10},
     doi = {10.4171/jems/818},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/818/}
}
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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

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