Wild ramification

Definition

Let $K$ be a discretely valued field and let $P_K$ be the wild inertia subgroup of its absolute Galois group. An étale representation, or the corresponding étale local system, is wildly ramified if $P_K$ acts nontrivially.

The ramification filtration on $P_K$ and its Swan conductor measure the depth of wild ramification. This étale notion is distinct from, though analogous to, the Stokes phenomena of an irregular complex connection.