The Rost invariant has trivial kernel for quasi-split groups of low rank

DOI10.1007/s00014-001-8325-8zbMath1001.20042arXivmath/0009162OpenAlexW2103421308MaRDI QIDQ5956907

Ryan Skip Garibaldi

Publication date: 24 September 2002

Published in: Commentarii Mathematici Helvetici (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0009162

zbMATH Keywords

algebraic groupsGalois cohomologyexceptional groupsquasi-split groupsRost invariantsSerre's conjecture II

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Exceptional (super)algebras (17B25) Cohomology theory for linear algebraic groups (20G10) Finite-dimensional division rings (16K20) (K)-theory of schemes (19E08) Galois cohomology of linear algebraic groups (11E72)

Related Items

Structure Theorems for Jordan Algebras of Degree Three Over Fields of Arbitrary Characteristic, Motivic construction of cohomological invariants, Degree three unramified cohomology of adjoint semisimple groups, Rost invariant of the center, revisited, The slice method for \(G\)-torsors, Killing forms of isotropic Lie algebras, Restricting the Rost invariant to the center, Zero cycles of degree one on principal homogeneous spaces, Splitting fields for \(E_8\)-torsors, Unramified cohomology of classifying varieties for exceptional simply connected groups, Serre’s Conjecture II: A Survey, Cohomological Invariants of Central Simple Algebras with Involution, On the Kernel of the Rost Invariant for E 8 Modulo 3, A rational construction of Lie algebras of type \(E_{7}\), Generically split projective homogeneous varieties, $E_8$, the most exceptional group, On the notion of canonical dimension for algebraic groups, Unnamed Item, Shells of twisted flag varieties and the Rost invariant

Cites Work

• Involutive automorphisms of root systems
• On the classification of Freudenthal triple systems and Lie algebras of type \(E_7\)
• Spinors of 13-dimensional space
• Isotopes of some nonassociative algebras with involution
• Isotropic trialitarian algebraic groups
• Galois Cohomology
• Rost's cohomological invariants in positive characteristic
• On Hjelmslev-Moufang planes
• Lie algebras of type \(E_6\)
• On restricted roots of semi-simple algebraic groups
• Canonical form and stationary subalgebras of points of general position for simple linear Lie groups
• Formes antihermitiennes devenant hyperboliques sur un corps de déploiement
• THE NORM RESIDUE HOMOMORPHISM OF DEGREE THREE
• Some Groups of Transformations defined by Jordan Algebras. I.
• The Arason invariant and mod 2 algebraic cycles
• Some groups of type D4 defined by Jordan algebras.
• Some groups of Transformations defined by Jordan Algebras. III. Groups of Type E61.
• The Freudenthal-Springer-Tits Constructions of Exceptional Jordan Algebras
• Groups of type E7.
• A Classification of Spinors Up to Dimension Twelve
• Strictly Regular Elements in Freudenthal Triple Systems
• Clifford algebras of hyperbolic involutions
• Hermitian analogue of a theorem of Springer
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item