The norm principle for type 𝐷_{𝑛} groups over complete discretely valued fields

Bhaskhar, Nivedita; Chernousov, Vladimir; Merkurjev, Alexander

doi:10.1090/tran/7558

The norm principle for type $D_n$ groups over complete discretely valued fields
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by Nivedita Bhaskhar, Vladimir Chernousov and Alexander Merkurjev PDF

Trans. Amer. Math. Soc. 372 (2019), 97-117 Request permission

Abstract:

Let $K$ be a complete discretely valued field with residue field $k$ with $\mathrm {char}(k)\neq 2$. Assuming that the norm principle holds for extended Clifford groups $\Omega (q)$ for every even dimensional nondegenerate quadratic form $q$ defined over any finite extension of $k$, we show that it holds for extended Clifford groups $\Omega (Q)$ for every even dimensional nondegenerate quadratic form $Q$ defined over $K$.

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