Hostname: page-component-77c89778f8-vsgnj Total loading time: 0 Render date: 2024-07-21T15:00:20.054Z Has data issue: false hasContentIssue false
  • English
  • Français

Another Proof of Totaro's Theorem on E8-Torsors

Published online by Cambridge University Press:  20 November 2018

Vladimir Chernousov
Vladimir Chernousov*
Affiliation:
Department of Mathematical Sciences, University of Alberta, Edmonton AB, T6G 2G1 e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We give a short proof of Totaro's theorem that every ${{E}_{8}}$-torsor over a field $k$ becomes trivial over a finite separable extension of $k$ of degree dividing $d\left( {{E}_{g}} \right)={{2}^{6}}{{3}^{2}}5$.

Keywords

11E7214M1720G15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 49 , Issue 2 , 01 June 2006 , pp. 196 - 202
Copyright
Copyright © Canadian Mathematical Society 2006

References

[1] Bourbaki, N., Éléments de mathématique. In: Groupes et algèbres de Lie, Ch. 4–6. Masson, Paris, 1981.Google Scholar
[2] Chernousov, V., 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 . Math. Ann. 326(2003), 297–330.Google Scholar
[3] Garibaldi, R. S., The Rost invariant has trivial kernel for quasi-split groups of low rank. Comment. Math. Helv. 76(2001), no. 4, 684–711.Google Scholar
[4] Garibaldi, S., Merkurjev, A., and Serre, J.-P., Cohomological Invariants in Galois Cohomology. University Lecture Series 28, American Mathematical Society, Providence, RI, 2003.Google Scholar
[5] Tits, J., Classification of algebraic semisimple groups. In: Algebraic Groups and Discontinuous Subgroups, Proc. Symp. Pure Math. 9, 1966, pp. 33–62.Google Scholar
[6] Tits, J., Sur les degrés des extensions de corps déployant les groupes algébriques simples. C. R. Acad. Sci. Paris Sr. I Math. 315(1992), no. 11, 1131–1138.Google Scholar
[7] Totaro, B., Splitting fields for E 8 -torsors. Duke Math. J. 121(2004), no. 3, 425–455.Google Scholar
[8] Totaro, B., The torsion index of E 8 and other groups. Duke Math. J. 129(2005), no. 2, 219–248.Google Scholar