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It is known (see here) that the absolute Galois group of a $p$-adic number field $K$ (ie a finite extension of $\mathbb Q_p$) is topologically finitely presented for any odd prime $p$.

Is it also true of the inertia subgroup, $\operatorname{Gal}(\bar K/K^{\rm unr})$, where $\bar K$ is the algebraic closure of $K$ and $K^\rm{unr}$ its maximal unramified extension ?

I know that the presentation cited in the above reference is explicit (so I could check if a lift of the Frobenius automorphism is given as one of the generators, and in that case it would be enough to omit it), but I don't know enough German (in which the original paper is written) to understand it.

I would be thankful for any given reference.

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