Frobenian multiplicative functions and rational points in fibrations

  • Daniel Loughran

    University of Bath, UK
  • Lilian Matthiesen

    KTH, Stockholm, Sweden
Frobenian multiplicative functions and rational points in fibrations cover
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Abstract

We consider the problem of counting the number of varieties in a family over with a rational point. We obtain lower bounds for this counting problem for some families over , even if the Hasse principle fails. We also obtain sharp results for some multinorm equations and for specialisations of certain Brauer group elements on higher-dimensional projective spaces, where we answer some cases of a question of Serre. Our techniques come from arithmetic geometry and additive combinatorics.

Cite this article

Daniel Loughran, Lilian Matthiesen, Frobenian multiplicative functions and rational points in fibrations. J. Eur. Math. Soc. 26 (2024), no. 12, pp. 4779–4830

DOI 10.4171/JEMS/1374