For G a simple simply connected algebraic group defined over a field F, Rost has shown that there exists a canonical map . This includes the Arason invariant for quadratic forms and Rost's mod 3 invariant for exceptional Jordan algebras as special cases. We show that RG has trivial kernel if G is quasi-split of type E6 or E7. A case-by-case analysis shows that it has trivial kernel whenever G is quasi-split of low rank.
Cite this article
R. S. Garibaldi, The Rost invariant has trivial kernel for quasi-split groups of low rank. Comment. Math. Helv. 76 (2001), no. 4, pp. 684–711DOI 10.1007/S00014-001-8325-8