Skip Garibaldi: The Rost invariant has trivial kernel for quasi-split groups of low rank and

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 RG: H1(F, G) --> H3(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 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. Thanks to a result by Gille, this holds in all characteristics.

1991 Mathematics Subject Classification: 20G10 (17B25)

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