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The following is a known result in algebraic geometry: Let $k$ be an algebraically closed field of characteristic zero (for example, $k=\mathbb{C}$). Let $L$ be a field such that $k \subset L \subset ...

Let $k$ be a field of characteristic zero and $I$ be a radical ideal of $k[[x_1,\ldots, x_n]]$. Let $P$ be a minimal prime ideal of the reduced ring $R:=k[[x_1,\ldots, x_n]]/I$. Then, $R_P$ is a field ...