Schinzel Hypothesis on average and rational points
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Published version
Author(s)
Skorobogatov, Alexei N
Sofos, Efthymios
Type
Journal Article
Abstract
We resolve Schinzel’s Hypothesis (H) for 100% of polynomials of arbitrary degrees. We deduce that a positive proportion of diagonal conic bundles over Q with any given number of degenerate fibres have a rational point, and obtain similar results for generalised Châtelet equations.
Date Issued
2023-02-01
Date Acceptance
2022-08-18
Citation
Inventiones Mathematicae, 2023, 231, pp.673-739
ISSN
0020-9910
Publisher
Springer
Start Page
673
End Page
739
Journal / Book Title
Inventiones Mathematicae
Volume
231
Copyright Statement
© The Author(s) 2022. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
License URL
Identifier
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Subjects
Science & Technology
Physical Sciences
Mathematics
HASSE PRINCIPLE
2 QUADRICS
PRIMES
INTERSECTIONS
PROGRESSIONS
VALUES
Publication Status
Published
Date Publish Online
2022-09-28