Trialitarian groups and the Hasse principle
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Let F be a field of characteristic ≠ 2 such that \(\) is of cohomological 2- and 3-dimension ≤ 2. For G a simply connected group of type 3 D 4 or 6 D 4 over F, we show that the natural map
where Ω F is the set of orderings of F and F v denotes the completion of F at v, restricts to be injective on the image of H 1(F, Z(G)) in H 1(F, G).
For F not formally real, this implies that Serre's “Conjecture II” [Ser.94,III.3.1] holds for such groups if and only if trialitarian groups are classified by their Tits algebras over F.
Mathematics Subject Classification (1991):Primary 11E72; Secondary 20G10, 20G15, 14M20, 17B25
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© Springer-Verlag Berlin Heidelberg 1999