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

R. Skip Garibaldi
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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.

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R. Skip Garibaldi. 2000-10-31. The Rost invariant has trivial kernel for quasi-split groups of low rank. https://arxiv.org/abs/math/0009162

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