The elementary obstruction and homogeneous spaces

DOI10.1215/S0012-7094-08-14124-9zbMath1135.14013arXivmath/0611700WikidataQ57395846 ScholiaQ57395846MaRDI QIDQ2472321

Alexei N. Skorobogatov, Jean-Louis Colliot-Thélène, Mikhail Borovoi

Publication date: 21 February 2008

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

Full work available at URL: https://arxiv.org/abs/math/0611700

zbMATH Keywords

homogeneous spaceBrauer groupelementary obstruction

Mathematics Subject Classification ID

Homogeneous spaces and generalizations (14M17) Galois cohomology (12G05) Rational points (14G05) Arithmetic algebraic geometry (Diophantine geometry) (11G99) Arithmetic ground fields for abelian varieties (14K15) Brauer groups of schemes (14F22) Galois cohomology of linear algebraic groups (11E72) Linear algebraic groups and related topics (20G99)

Related Items (18)

The étale Brauer-Manin obstruction to strong approximation on homogeneous spaces ⋮ Progress concerning the local-global principle for zero-cycles on algebraic varieties ⋮ Galois sections for abelianized fundamental groups ⋮ The étale fundamental group of a homogeneous space of a linear algebraic group ⋮ Rational points of rationally simply connected varieties over global function fields ⋮ Supersolvable descent for rational points ⋮ A formular for the algebraic Brauer groups of torsor ⋮ Extended equivariant Picard complexes and homogeneous spaces ⋮ HOMOGENEOUS SPACE FIBRATIONS OVER SURFACES ⋮ Local-global principles for 1-motives ⋮ On Albanese torsors and the elementary obstruction ⋮ On abelian birational sections ⋮ Lois de réciprocité supérieures et points rationnels ⋮ Complex multiplication and Brauer groups of \(K3\) surfaces ⋮ Extended Picard complexes and linear algebraic groups ⋮ The elementary obstruction and the Weil restriction ⋮ Le principe de Hasse pour les espaces homogènes : réduction au cas des stabilisateurs finis ⋮ Implications of the Hasse principle for zero cycles of degree one on principal homogeneous spaces

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