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Let $A$ be a strictly henselian discrete valuation ring. What is $\pi_1(\operatorname{Spec}(A) \setminus \{s\})$?

I thought it is a semidirect product of a pro-$p$-group (the wild ramification group) and $\hat{\mathbf{Z}}'(1)$ (the tame fundamental group), but it is claimed that it is only the tame fundamental group.

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