完备离散值域上$D_n$型群的范数原理
The norm principle for type $D_n$ groups over complete discretely valued fields
摘要：
设$K$是一个完备的离散域，其剩余域$k$具有$\mathrm{char}(k)\neq 2$ .假设范数原理对扩展Clifford群$Ω(q)$对定义在$k$的任意有限扩张上的每个偶数维非退化二次型$q$成立，证明了范数原理对扩展Clifford群$Ω(Q)$对定义在$K$上的每个偶数维非退化二次型$Q$成立.
英文摘要：
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 $Ω(q)$ for every even dimensional non-degenerate quadratic form $q$ defined over any finite extension of $k$, we show that it holds for extended Clifford groups $Ω(Q)$ for every even dimensional non-degenerate quadratic form $Q$ defined over $K$.
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