Local-global principles for 1-motives

DOI10.1215/00127094-2008-028zbMath1155.14020arXivmath/0703845OpenAlexW2039896967MaRDI QIDQ935197

Tamás Szamuely, David Harari

Publication date: 5 August 2008

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0703845

zbMATH Keywords

1-motiveHasse principleBrauer grouptorsorsemiabelian varietyManin obstruction

Mathematics Subject Classification ID

Global ground fields in algebraic geometry (14G25)

Related Items (15)

The étale Brauer-Manin obstruction to strong approximation on homogeneous spaces ⋮ Progress concerning the local-global principle for zero-cycles on algebraic varieties ⋮ Duality theorems for function fields over higher local fields ⋮ Galois sections for abelianized fundamental groups ⋮ On analogs of Cassels-Tate's exact sequence for connected reductive groups and Brauer-Manin obstruction for homogeneous spaces over global function fields ⋮ A formular for the algebraic Brauer groups of torsor ⋮ Arithmetics of homogeneous spaces over p$p$‐adic function fields ⋮ Degree and the Brauer-Manin obstruction ⋮ The elementary obstruction and homogeneous spaces ⋮ On Albanese torsors and the elementary obstruction ⋮ On abelian birational sections ⋮ The Brauer–Manin obstruction for integral points on curves ⋮ Local-global questions for tori over 𝑝-adic function fields ⋮ Dualité et principe local-global pour les tores sur une courbe au-dessus de ℂ((t )) ⋮ Unnamed Item

Cites Work

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• La descente sur les variétés rationnelles. II. (The descent on rational varieties. II)
• The elementary obstruction and homogeneous spaces
• On Albanese torsors and the elementary obstruction
• Commutative group schemes
• Théorie de Hodge. III
• On the Brauer–Manin obstruction for zero-cycles on curves
• Extended Picard complexes and linear algebraic groups
• Groupe de Brauer et arithmétique des groupes algébriques linéaires sur un corps de nombres.
• Néron Models
• Arithmetic Duality Theorems for 1-Motives
• The Manin obstruction for torsors under connected algebraic groups
• Duality of Albanese and Picard 1-motives

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