The kernel of the Rost invariant, Serre's Conjecture II and the Hasse principle for quasi-split groups 3,6D 4 ,E 6 ,E 7
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We prove that for a simple simply connected quasi-split group of type 3,6D 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 3,6D 4 ,E 6 ,E 7 .
KeywordsStrong Result Exceptional Group Hasse Principle Perfect Field Trivial Kernel
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