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A pure cubic field is an algebraic number field of the form $K = \mathbb{Q}(\theta)$ with $\theta^3 = m$, $m \neq \pm 1$. What can be said about the parity (odd or even) of the class number of a pure ...

I am trying to understand the proof of the following result: Suppose $F$ is a function field in $k$ variables over an algebraically closed field. Let $f_1,...,f_r \in F[x_1,...,x_n]$ be ...