Frobenian multiplicative functions and rational points in fibrations

Daniel Loughran, Lilian Matthiesen

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the problem of counting the number of varieties in a family over Q with a rational point. We obtain lower bounds for this counting problem for some families over P1, 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.
Original languageEnglish
JournalJournal of the European Mathematical Society
DOIs
Publication statusPublished - 16 Sept 2023

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