COUNTEREXAMPLES TO THE HASSE PRINCIPLE IN FAMILIES

DOI10.1017/S0004972721000885zbMath1505.11052OpenAlexW3214691140WikidataQ124935182 ScholiaQ124935182MaRDI QIDQ5097514

Nguyen Xuan Tho

Publication date: 25 August 2022

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0004972721000885

zbMATH Keywords

Hasse principleBrauer-Manin obstructiondiagonal quartic surfaces

Mathematics Subject Classification ID

Diophantine equations in many variables (11D72) Cubic and quartic Diophantine equations (11D25) Hasse principle, weak and strong approximation, Brauer-Manin obstruction (14G12)

Cites Work

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• Beyond the Manin obstruction. -- Appendix A by S. Siksek: 4-descent. -- Appendix B: The Grothendieck spectral sequence and the truncation functor
• An explicit algebraic family of genus-one curves violating the Hasse principle
• Counterexamples to the local-global principle associated with Swinnerton-Dyer's cubic form
• Brauer groups of diagonal quartic surfaces
• The Diophantine equation \(ax^3+by^3+cz^3=0\)
• The Brauer–Manin obstruction on a general diagonal quartic surface
• On the Hasse principle for certain quartic hypersurfaces
• Arithmetic of diagonal quartic surfaces, II
• An interesting quartic surface, everywhere locally solvable, with cubic point but no global point
• On the Hasse principle for cubic surfaces
• Einige im Kleinen überall lösbare, im Großen unlösbare diophantische Gleichungen.

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