The Rost invariant has trivial kernel for quasi-split groups of low rank
Group Theory
2007-05-23 v2 Rings and Algebras
Abstract
For G an almost simple simply connected algebraic group defined over a field F, Rost has shown that there exists a canonical map R_G: H^1(F, G) --> H^3(F, Q/Z(2)). This includes the Arason invariant for quadratic forms and Rost's mod 3 invariant for Albert algebras as special cases. We show that R_G has trivial kernel if G is quasi-split of type E_6 or E_7. A case-by-case analysis shows that it has trivial kernel whenever G is quasi-split of low rank.
Keywords
Cite
@article{arxiv.math/0009162,
title = {The Rost invariant has trivial kernel for quasi-split groups of low rank},
author = {R. Skip Garibaldi},
journal= {arXiv preprint arXiv:math/0009162},
year = {2007}
}
Comments
Author-supplied DVI/PS files available at http://www.math.ucla.edu/~skip/preprints.html Minor changes since first edition