Abstract.
We prove that for a simple simply connected quasi-split group of type 3,6 D 4 ,E 6 ,E 7 defined over a perfect field F of characteristic ≠=2,3 the Rost invariant has trivial kernel. In certain cases we give a formula for the Rost invariant. It follows immediately from the result above that if cd F≤2 (resp. vcd F≤2) then Serre's Conjecture II (resp. the Hasse principle) holds for such a group. For a (C 2 )-field, in particular ℂ(x,y), we prove the stronger result that Serre's Conjecture II holds for all (not necessary quasi-split) exceptional groups of type 3,6 D 4 ,E 6 ,E 7 .
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Received: 27 March 2002 / Published online: 28 March 2003
The author gratefully acknowledge the support of TMR ERB FMRX CT-97-0107 and Forschungsinstitut für Mathematik, ETH in Zürich
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Chernousov, V. The kernel of the Rost invariant, Serre's Conjecture II and the Hasse principle for quasi-split groups 3,6 D 4 ,E 6 ,E 7 . Math. Ann. 326, 297–330 (2003). https://doi.org/10.1007/s00208-003-0417-x
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DOI: https://doi.org/10.1007/s00208-003-0417-x