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

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  • Authors:
  • Daniel Loughran


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.

Bibliographical metadata

Original languageEnglish
Pages (from-to)2539-2588
Number of pages50
JournalJournal of the European Mathematical Society
Issue number10
Early online date20 Jul 2018
Publication statusPublished - 2018