Some varieties with points only in a field extension

DOI10.1007/BF01196658zbMath0532.14011MaRDI QIDQ788781

D. J. Lewis, Andrew Bremner, Patrick Morton

Publication date: 1984

Published in: Archiv der Mathematik (Search for Journal in Brave)

zbMATH Keywords

quartic curvecubic field extensioncubicsexistence of rational points on varieties

Mathematics Subject Classification ID

Arithmetic ground fields for curves (14H25) Cubic and quartic Diophantine equations (11D25) Global ground fields in algebraic geometry (14G25)

Related Items (8)

Algebraic points on quartic curves over function fields ⋮ Solutions to \(x^4+py^4=z^4\) in cubic number fields ⋮ Some interesting curves of genus 2 to 7 ⋮ The Brauer-Manin obstruction for sections of the fundamental group ⋮ The Hasse principle and the Brauer-Manin obstruction for curves ⋮ The arithmetic of certain quartic curves ⋮ The arithmetic of certain quartic curves ⋮ On the Hasse principle for certain quartic hypersurfaces

Cites Work

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• A new characterization of the integer 5906
• On a problem of Pfister about systems of quadratic forms
• Algebraic points on cubic hypersurfaces
• Homogeneous additive equations

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