skip@member.ams.org and http://www.math.ucla.edu/~skip/

Submission: 2000, Oct 31

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. Thanks to a result by Gille, this holds in all
characteristics.

1991 Mathematics Subject Classification: 20G10 (17B25)

Keywords and Phrases:

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