Progress concerning the local-global principle for zero-cycles on algebraic varieties

DOI10.1216/RMJ-2016-46-4-1293zbMath1358.11073OpenAlexW2538084984MaRDI QIDQ329924

Yongqi Liang

Publication date: 24 October 2016

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmjm/1476884584

zbMATH Keywords

weak approximationHasse principlezero-cyclesBrauer and Manin's obstruction

Mathematics Subject Classification ID

Varieties over global fields (11G35) Algebraic cycles (14C25) Global ground fields in algebraic geometry (14G25)

Cites Work

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• Towards the Brauer-Manin obstruction on varieties fibred over the projective line
• The local-global principle for zero cycles on certain fibrations over a curve. I.
• Zero cycles on fibrations over a curve of arbitrary genus
• Some observations on motivic cohomology of arithmetic schemes
• Local-global principles for 1-motives
• Insufficiency of the Brauer-Manin obstruction applied to étale covers
• On the Chow groups of certain rational surfaces: a sequel to a paper of S. Bloch
• Zero-cycles on rational surfaces over number fields
• Beyond the Manin obstruction. -- Appendix A by S. Siksek: 4-descent. -- Appendix B: The Grothendieck spectral sequence and the truncation functor
• Fibration method and Manin obstruction
• Rational solutions of certain equations involving norms
• The arithmetic of the Chow group of zero-cycles
• Universal torsors and values of quadratic polynomials represented by norms
• The local-global exact sequence for Chow groups of zero-cycles
• The elementary obstruction and homogeneous spaces
• A NOTE ON A THEOREM OF HEATH-BROWN AND SKOROBOGATOV
• Singular curves and the étale Brauer-Manin obstruction for surfaces
• Principe local-global pour les zéro-cycles sur certaines fibrations au-dessus de l'espace projectif
• On the equation N _{K /k} (Ξ)=P (t )
• On the Brauer–Manin obstruction for zero-cycles on curves
• Flèches de spécialisations en cohomologie étale et applications arithmétiques
• Obstruction de Brauer-Manin pour les zéro-cycles sur des fibrations en variétés de Severi-Brauer
• THE BRAUER–MANIN OBSTRUCTION FOR ZERO-CYCLES ON SEVERI–BRAUER FIBRATIONS OVER CURVES
• Principe local-global pour les zéro-cycles sur les surfaces réglées
• The Brauer-Manin obstructions for homogeneous spaces with connected or abelian stabilizer.
• Arithmetic of 0-cycles on varieties defined over number fields
• Local-global principle for certain biquadratic normic bundles
• Astuce de Salberger et Zéro-cycles Sur Certaines Fibrations
• Spécialisation des conditions de Manin pour les variétés fibrées au-dessus de l'espace projectif

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