𝑅-equivalence in spinor groups

Chernousov, Vladimir; Merkurjev, Alexander

doi:10.1090/S0894-0347-01-00365-4

$R$-equivalence in spinor groups
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by Vladimir Chernousov and Alexander Merkurjev PDF

J. Amer. Math. Soc. 14 (2001), 509-534 Request permission

Abstract:

The groups of $R$-equivalent classes of the spinor groups of non-degenerate quadratic forms over arbitrary fields are computed in terms of certain $K$-cohomology groups of corresponding quadric hypersurfaces. As an application, examples of non-rational spinor groups of every dimension $\geq 6$ are given.

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