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
JournalJournal of the European Mathematical Society
Early online date20 Jul 2018
StatePublished - 2018