Let $F$ be a $p$-adic field of characteristic 0. Is it always possible to find a number field $K$ such that $K$ has only one place lying above $p$ and such that its completion at this place is $F$?
If so, is there any reference for this?
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3$\begingroup$ This follows easily from Krasner's lemma. $\endgroup$– David LoefflerCommented Nov 28, 2020 at 12:00
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2$\begingroup$ Does this answer your question? “Algebraization" of $p$-adic fields $\endgroup$– David LoefflerCommented Nov 28, 2020 at 14:39
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