Definition 59.67.5. A field $K$ is called $C_ r$ if for every $0 < d^ r < n$ and every $f \in K[T_1, \ldots , T_ n]$ homogeneous of degree $d$, there exist $\alpha = (\alpha _1, \ldots , \alpha _ n)$, $\alpha _ i \in K$ not all zero, such that $f(\alpha ) = 0$. Such an $\alpha$ is called a nontrivial solution of $f$.

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• 3 comment(s) on Section 59.67: Galois cohomology

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