Relative Weil group ($W(L/K)$)

For a Galois extension $L/K$ of non-Archimedean local fields, the relative Weil group consists of the automorphisms whose residue action is an integral power of Frobenius. It fits intowhen the residue extension is the full algebraic extension.

The Weil-group topology makes the inertia group open with its profinite topology and makes the quotient by inertia discrete. It is generally finer than the topology induced from the ambient Galois group.