Tamely ramified extension

A finite extension of local fields is tamely ramified when its residue-field extension is separable and its ramification index is coprime to the residue characteristic. For a finite Galois extension this is equivalent to trivial wild inertia group $G_1$.

If $L/K$ is a finite tamely ramified Galois extension of local fields with degree $n$ and ramification index $e$, then its different exponent is $e-1$ and the discriminant exponent is