The solubility of diagonal cubic surfaces

DOI10.1016/S0012-9593(01)01080-1zbMath1003.11028OpenAlexW2104103380MaRDI QIDQ4534276

H. P. F. Swinnerton-Dyer

Publication date: 14 August 2002

Published in: Annales Scientifiques de l’École Normale Supérieure (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=ASENS_2001_4_34_6_891_0

zbMATH Keywords

elliptic curveTate-Shafarevich groupHasse principleprojective diagonal cubic surface

Mathematics Subject Classification ID

Forms of degree higher than two (11E76) Rational points (14G05) Varieties over global fields (11G35) Arithmetic ground fields for surfaces or higher-dimensional varieties (14J20) Cubic and quartic Diophantine equations (11D25)

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Rational Points on Diagonal Cubic Surfaces, Unnamed Item, Une liste de problèmes, MANY CUBIC SURFACES CONTAIN RATIONAL POINTS, Random Diophantine equations. I, Integral points on conic log K3 surfaces, Cubic forms in 14 variables, 2-descent on elliptic curves and rational points on certain Kummer surfaces, Rational points on cubic hypersurfaces over \(\mathbb F_q(t)\)

Cites Work

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• Hasse principle for pencils of curves of genus one whose Jacobians have rational 2-division points
• Solubility of Certain Pencils of Curves of Genus 1, and of the Intersection of two Quadrics in P⁴
• Arithmetic on Curves of Genus 1. I. On a conjecture of Selmer.
• The Solubility of Diagonal Cubic Diophantine Equations
• On the Hasse principle for cubic surfaces
• Sufficient congruence conditions for the existence of rational points on certain cubic surfaces