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Mathematische Annalen

, Volume 326, Issue 2, pp 297–330 | Cite as

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

  • V. Chernousov

Abstract.

 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 .

Keywords

Strong Result Exceptional Group Hasse Principle Perfect Field Trivial Kernel 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

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

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