Failures of weak approximation in families

DOI10.1112/S0010437X16007405zbMath1348.14067arXiv1506.01817MaRDI QIDQ2816797

M. J. Bright, Timothy D. Browning, Daniel Loughran

Publication date: 25 August 2016

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.01817

zbMATH Keywords

rational pointsweak approximationfibrationBrauer-Manin obstructionfamilies of varietiesalmost-all

Mathematics Subject Classification ID

Rational points (14G05) Arithmetic ground fields (finite, local, global) and families or fibrations (14D10) Varieties over global fields (11G35) Cubic and quartic Diophantine equations (11D25) Global ground fields in algebraic geometry (14G25)

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Cites Work

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• Manin's conjecture for certain biprojective hypersurfaces
• Forms in many variables and differing degrees
• On Manin's conjecture for a family of Châtelet surfaces
• La conjecture de Weil. II
• Cohomologie étale. Seminaire de géométrie algébrique du Bois-Marie SGA 4 1/2 par P. Deligne, avec la collaboration de J. F. Boutot, A. Grothendieck, L. Illusie et J. L. Verdier
• Fibration method and Manin obstruction
• Semialgebraic sets and some versions of the Tarski-Seidenberg-Macintyre theorem
• The Cassels-Tate pairing on polarized Abelian varieties
• The number of varieties in a family which contain a rational point
• Strong approximation and descent
• The proportion of plane cubic curves over ℚ that everywhere locally have a point
• ON THE BRAUER GROUP OF DIAGONAL CUBIC SURFACES
• On the Brauer–Manin obstruction for degree-four del Pezzo surfaces
• O-minimality on twisted universal torsors and Manin's conjecture over number fields
• Heights in number fields
• La $R$-équivalence sur les tores
• Flèches de spécialisations en cohomologie étale et applications arithmétiques
• Tamagawa numbers of diagonal cubic surfaces, numerical evidence
• Descent on fibrations over the projective line
• Lipschitz² : A New Version of an Old Principle
• Bad reduction of the Brauer-Manin obstruction
• Number of Points of Varieties in Finite Fields
• Number fields