Grothendieck’s theorem on non-abelian 𝐻² and local-global principles

DOI10.1090/S0894-0347-98-00271-9zbMath0893.14015arXivmath/9803113OpenAlexW1776906052WikidataQ102731083 ScholiaQ102731083MaRDI QIDQ4396478

Claus Scheiderer, R. Sujatha, Yuval Z. Flicker

Publication date: 14 June 1998

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9803113

zbMATH Keywords

homogeneous spacesreal spectrumlocal-global principlenon-abelian \(H^2\)-cohomology sets of algebraic groups

Mathematics Subject Classification ID

Étale and other Grothendieck topologies and (co)homologies (14F20) Cohomology theory for linear algebraic groups (20G10) Galois cohomology (11R34) Forms over real fields (11E10)

Related Items (16)

Homogeneous spaces, algebraic \(K\)-theory and cohomological dimension of fields ⋮ Arithmetic of linear algebraic groups over 2-dimensional geometric fields ⋮ Twisted forms of toric varieties ⋮ On homogeneous spaces with finite anti-solvable stabilizers ⋮ Extensions of algebraic groups with finite quotient and nonabelian 2-cohomology ⋮ Equivariant models of spherical varieties ⋮ On the homogeneous spaces of Borovoi-Kunyavskii ⋮ Local-global principles for homogeneous spaces of reductive groups over global function fields ⋮ Arithmetics of homogeneous spaces over p$p$‐adic function fields ⋮ Comparing descent obstruction and Brauer-Manin obstruction for open varieties ⋮ Real structures on nilpotent orbit closures ⋮ Non-ramified Brauer group of homogeneous spaces with finite stabilisers ⋮ Espaces homogènes génériquement triviaux ⋮ Le principe de Hasse pour les espaces homogènes : réduction au cas des stabilisateurs finis ⋮ Real reductive Cayley groups of rank 1 and 2. ⋮ Unramified algebraic Brauer group of homogeneous spaces

Cites Work

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• Closed subgroups of G(Q) with involutions
• Classical groups and the Hasse principle.
• Abelianization of the second nonabelian Galois cohomology
• Galois cohomology of the classical groups over fields of cohomological dimension \(\leq 2\)
• Hasse principles and approximation theorems for homogeneous spaces over fields of virtual cohomological dimension one
• Théoremes de finitude en cohomologie galoisienne
• Some Basic Theorems on Algebraic Groups
• Abelian Galois cohomology of reductive groups
• Groupes linéaires sur le corps de fonctions de courbes réelles.
• Approximation Theory and the Rank of Abelian Varieties Over Large Algebraic Fields
• Homology

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