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COUNTEREXAMPLES TO THE HASSE PRINCIPLE IN FAMILIES

Part of: Diophantine equations

Published online by Cambridge University Press:  05 November 2021

NGUYEN XUAN THO Open the ORCID record for NGUYEN XUAN THO [Opens in a new window]
NGUYEN XUAN THO*
Affiliation:
School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, Hanoi, Vietnam
*
e-mail: tho.nguyenxuan1@hust.edu.vn
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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.

Keywords

Brauer–Manin obstructionHasse principlediagonal quartic surfaces

MSC classification

Primary: 11D25: Cubic and quartic equations
Secondary: 11D88: $p$-adic and power series fields
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 106 , Issue 1 , August 2022 , pp. 18 - 27
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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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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