𝑅-equivalence in spinor groups

DOI10.1090/S0894-0347-01-00365-4zbMath0998.20042OpenAlexW1585403517MaRDI QIDQ2719029

Alexander S. Merkurjev, Vladimir I. Chernousov

Publication date: 14 May 2001

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

Full work available at URL: https://doi.org/10.1090/s0894-0347-01-00365-4

zbMATH Keywords

quadratic formsalgebras with involutionsspinor groupsClifford groups\(R\)-equivalencerational morphismsrationality problem for algebraic groups

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Quadratic forms over general fields (11E04) Classical groups (algebro-geometric aspects) (14L35) Finite-dimensional division rings (16K20) Higher symbols, Milnor (K)-theory (19D45) Applications of methods of algebraic (K)-theory in algebraic geometry (14C35)

Related Items (8)

The group SK 2 of a biquaternion algebra ⋮ Spécialisation de la $R$-équivalence pour les groupes réductifs ⋮ The group of \(K_{1}\)-zero-cycles on the second generalized Severi-Brauer variety of an algebra of index 4 ⋮ Pathologies of the group of R-equivalence classes of a linear algebraic groups ⋮ The group \(SK_{2}\) of a biquaternion algebra ⋮ Zero-cycles with coefficients for the second generalized symplectic involution variety of an algebra of degree 4 ⋮ Automorphisms of Albert algebras and a conjecture of Tits and Weiss II ⋮ R‐triviality of groups of type F4 arising from the first Tits construction

Cites Work

• K-theory of quadric hypersurfaces
• Locally trivial principal homogeneous spaces
• \(R\)-equivalence and special unitary groups
• A variety associated to an algebra with involution
• Chow groups with coefficients
• \(R\)-equivalence and rationality problem for semisimple adjoint classical algebraic groups
• The \(R\)-equivalence on reductive algebraic groups defined over a global field
• Generic element in \(SK_ 1\) for simple algebras
• Algebraic \(K\)-theory and quadratic forms. With an appendix by J. Tate
• K-cohomology of regular schemes
• Some theorems on the k-theory of coherent sheaves
• La $R$-équivalence sur les tores
• Invariants of algebraic groups
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