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### Possible failure of $ef=n$ for a degree $n$ extension of a field complete to a nondiscrete nonarchimedean valuation?

Let $T$ be the maximal tamely ramified extension of $\mathbb{Q}_p$ with $p>2$, and $K$ be the completion of $T_p=T(\mu_{p^{\infty}})$. It’s clear that $|K^{\times}|=p^{\mathbb{Q}}$: in particular, ...
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