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 |
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Authors: | V Chernousov |
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Institution: | (1) Forschungsinstitut für Mathematik, ETH–Zentrum, CH-8092 Zürich, Switzerland (e-mail: chernous@mathematik.uni-bielefeld.de), CH |
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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
.
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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Keywords: | |
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