Rational points on pencils of conics and quadrics with many degenerate fibres

DOI10.4007/annals.2014.180.1.8zbMath1296.14015arXiv1209.0207OpenAlexW2964315069WikidataQ57395837 ScholiaQ57395837MaRDI QIDQ2251007

Alexei N. Skorobogatov, Lilian Matthiesen, Timothy D. Browning

Publication date: 10 July 2014

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.0207

zbMATH Keywords

rational pointweak approximationBrauer-Manin obstructionconic bundleZariski-dense

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09) Rational points (14G05) Arithmetic ground fields for surfaces or higher-dimensional varieties (14J20)

Related Items (15)

On the equation N _{K /k} (Ξ)=P (t ) ⋮ Strong approximation and descent ⋮ Average Bateman–Horn for Kummer polynomials ⋮ Une liste de problèmes ⋮ Supersolvable descent for rational points ⋮ Schinzel hypothesis on average and rational points ⋮ Brauer–Manin obstruction and families of generalised Châtelet surfaces over number fields ⋮ Point générique et saut du rang du groupe de Mordell–Weil ⋮ The Hardy–Littlewood conjecture and rational points ⋮ The value of polynomials represented by norm forms ⋮ On the fibration method for zero-cycles and rational points ⋮ Integral points on generalised affine Châtelet surfaces ⋮ Rational points on fibrations with few non-split fibres ⋮ The Brauer–Manin obstruction on Kummer varieties and ranks of twists of abelian varieties ⋮ Rational points and prime values of polynomials in moderately many variables

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