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COUNTEREXAMPLES TO THE HASSE PRINCIPLE IN FAMILIES
Part of:
Diophantine equations
Published online by Cambridge University Press: 05 November 2021
Abstract
We generalise two quartic surfaces studied by Swinnerton-Dyer to give two infinite families of diagonal quartic surfaces which violate the Hasse principle. Standard calculations of Brauer–Manin obstructions are exhibited.
MSC classification
Primary:
11D25: Cubic and quartic equations
Secondary:
11D88: $p$-adic and power series fields
- Type
- Research Article
- Information
- Copyright
- © The Author(s), 2021. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.
Footnotes
The author is supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) (grant number 101.04-2019.314).
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