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Article Dans Une Revue Journal für die reine und angewandte Mathematik Année : 2022

Rational points on fibrations with few non-split fibres

Résumé

We revisit the abstract framework underlying the fibration method for producing rational points on the total space of fibrations over the projective line. By fine-tuning its dependence on external arithmetic conjectures, we render the method unconditional when the degree of the non-split locus is $\leq 2$, as well as in various instances where it is $3$. We are also able to obtain improved results in the regime that is conditionally accessible under Schinzel's hypothesis, by incorporating into it, for the first time, a technique due to Harari for controlling the Brauer--Manin obstruction in families.

Dates et versions

hal-03360681 , version 1 (30-09-2021)

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Yonatan Harpaz, Dasheng Wei, Olivier Wittenberg. Rational points on fibrations with few non-split fibres. Journal für die reine und angewandte Mathematik, 2022, 2022 (791), pp.89-133. ⟨10.1515/crelle-2022-0042⟩. ⟨hal-03360681⟩
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