The kernel of the Rost invariant , Serre ’ s Conjecture II and the Hasse principle for quasi - split groups
نویسنده
چکیده
We prove that for a simple simply connected quasi-split group of type 3,6D4, E6, E7 defined over a perfect field F of characteristic 6= 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 cdF ≤ 2 (resp. vcdF ≤ 2) then Serre’s Conjecture II (resp. the Hasse principle) holds for such a group. For a (C2)-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 3,6D4, E6, E7.
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تاریخ انتشار 2008