On the Kernel of the Rost Invariant for E 8 Modulo 3

DOI10.1007/978-1-4419-6211-9_11zbMath1231.20046OpenAlexW2151863336MaRDI QIDQ3001254

Vladimir I. Chernousov

Publication date: 31 May 2011

Published in: Quadratic Forms, Linear Algebraic Groups, and Cohomology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-1-4419-6211-9_11

zbMATH Keywords

Rost invariantGalois descentfinite field extensionssplit groups of type \(E_8\)

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Cohomology theory for linear algebraic groups (20G10) Galois cohomology of linear algebraic groups (11E72) Exceptional groups (20G41) Structure theory for linear algebraic groups (20G07)

Related Items (5)

Local-global questions for tori over 𝑝-adic function fields ⋮ $E_8$, the most exceptional group ⋮ Unnamed Item ⋮ Generically split projective homogeneous varieties. II ⋮ Shells of twisted flag varieties and the Rost invariant

Cites Work

• The kernel of the Rost invariant, Serre's conjecture II and the Hasse principle for quasi-split groups \(^{3,6}D_4\), \(E_6\), \(E_7\).
• Splitting fields for \(E_8\)-torsors
• Remark on the Serre \((\text{mod }5)\)-invariant for groups of type \(E_ 8\)
• Regular elements of semisimple algebraic groups
• Lectures on Chevalley Groups
• Another Proof of Totaro's Theorem on E₈-Torsors
• The Rost invariant has trivial kernel for quasi-split groups of low rank
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