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Rational points on fibrations with few non-split fibres

  • Yonatan Harpaz , Dasheng Wei und Olivier Wittenberg EMAIL logo
Veröffentlicht/Copyright: 12. August 2022

Abstract

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 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.

Award Identifier / Grant number: 11622111

Award Identifier / Grant number: 11631009

Funding statement: The second-named author is supported by National Key R&D Program of China and National Natural Science Foundation of China (Grant Nos. 11622111 and 11631009).

Acknowledgements

We thank the anonymous referee for their helpful comments.

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Received: 2021-10-15
Revised: 2022-06-01
Published Online: 2022-08-12
Published in Print: 2022-10-01

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