The Rost invariant has trivial kernel for quasi-split groups of low rank

Details The Rost invariant has trivial kernel for quasi-split groups of low rank The Rost invariant has trivial kernel for quasi-split groups of low rank

2000-09-15

arxiv.org/abs/math/0009162v2

Comment. Math. Helv., vol. 76 (2001) 684-711

Mathematics

Group Theory

Author-supplied DVI/PS files available at http://www.math.ucla.edu/~skip/preprints.html Minor changes since first edition

Scientific paper

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.

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