Tame ramification

Definition

Let $K$ be a discretely valued field with inertia subgroup $I_K$ and wild inertia subgroup $P_K$. An étale representation, or the corresponding étale local system, is tamely ramified if

acts trivially. It may still have nontrivial action of the tame quotient $I_K/P_K$.

This étale definition should not be identified with regular singularity of a complex connection without invoking a comparison theorem.