Definition 15.112.6. With assumptions and notation as in Lemma 15.112.5.

The

*wild inertia group of $\mathfrak m$*is the subgroup $P$.The

*tame inertia group of $\mathfrak m$*is the quotient $I \to I_ t$.

We denote $\theta : I \to \mu _ e(\kappa (\mathfrak m))$ the surjective map (15.112.5.1) whose kernel is $P$ and which induces the isomorphism $I_ t \to \mu _ e(\kappa (\mathfrak m))$.

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