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.
| Original language | English |
|---|---|
| Pages (from-to) | 2539-2588 |
| Number of pages | 50 |
| Journal | Journal of the European Mathematical Society |
| Volume | 20 |
| Issue number | 10 |
| Early online date | 20 Jul 2018 |
| DOIs | |
| Publication status | Published - 2018 |
Keywords
- Brauer groups
- Families of varieties
- Rational points
- Toric varieties