低秩拟分裂群的Rost不变量具有平凡核
The Rost invariant has trivial kernel for quasi-split groups of low rank
摘要：
对域F上几乎单连通代数群G，Rost证明了存在一个标准映射R_G：H^1（F，G）--> H^3（F，Q/Z（2））.这包括作为特殊情况的二次型的Arason不变量和Albert代数的Rost模3不变量。证明了若G是E_6或E_7型拟分裂的，则R_G有平凡核.分析表明，当G是低秩拟分裂时，它具有平凡核。
英文摘要：
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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