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Pete L. Clark
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$\mathbb{P}_k^1$, over an algebraically closed field, is such an example. You can adapt the proof that $\mathbb{Q}$ has no unrammifiedunramified extensions to show that $k(t)$ has no unramified extensions.

$\mathbb{P}_k^1$, over an algebraically closed field, is such an example. You can adapt the proof that $\mathbb{Q}$ has no unrammified extensions to show that $k(t)$ has no unramified extensions.

$\mathbb{P}_k^1$, over an algebraically closed field, is such an example. You can adapt the proof that $\mathbb{Q}$ has no unramified extensions to show that $k(t)$ has no unramified extensions.

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David E Speyer
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$\mathbb{P}_k^1$, over an algebraically closed field, is such an example. You can adapt the proof that $\mathbb{Q}$ has no unrammified extensions to show that $k(t)$ has no unramified extensions.