Swan Conductor

The Swan conductor is the contribution from wild ramification to the Artin conductor of a finite-dimensional Galois representation. If is such a representation of the Galois group of a finite Galois extension of local fields and are the lower ramification groups, then

Here is the subspace fixed by . In particular, the Swan conductor vanishes when the wild inertia subgroup acts trivially on , i.e., when the representation has tame ramification.