On Brauer-Manin obstructions and analogs of Cassels-Tate's exact sequence for connected reductive groups over global function fields

DOI10.3792/pjaa.97.013zbMath1483.11068MaRDI QIDQ2075291

Nguyêñ Quôć Thǎńg

Publication date: 14 February 2022

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

zbMATH Keywords

Galois cohomologyBrauer groupsweak approximationreductive groupTate-Shafarevich kernellocal and global field

Mathematics Subject Classification ID

Local ground fields in algebraic geometry (14G20) Cohomology theory for linear algebraic groups (20G10) Galois cohomology of linear algebraic groups (11E72)

Related Items (2)

On analogs of Cassels-Tate's exact sequence for connected reductive groups and Brauer-Manin obstruction for homogeneous spaces over global function fields ⋮ A note on obstructions to weak approximation and Brauer and R-equivalence relations for homogeneous spaces over global fields

Cites Work

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• On some Hasse principles for homogeneous spaces of algebraic groups over global fields of positive characteristic
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• Résolutions flasques des groupes linéaires connexes
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• The Brauer-Manin obstructions for homogeneous spaces with connected or abelian stabilizer.
• A cohomological obstruction to weak approximation for homogeneous spaces
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