# Ramification group of valuations - need terminology

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1. Dec 19, 2014

### coquelicot

I am lost and need some terminology (also hopefully sources).
Let L/K be a Galois extension, and w be a valuation of a L, lying above a valuation v of K. Notice that I do not suppose that w is discrete.
Given α > 0 in the finite image of w, each of the following can easily been shown to be a subgroup of the inertia group of w in L :

* { σ ∈ Gal(L/K) : w(σ x - x) ≥ α },

* {σ ∈ Gal(L/K) : w(σ x - x) > α },

* { σ ∈ Gal(L/K) : w(σ x - x) ≥ w(x) + α },

* { σ ∈ Gal(L/K) : w(σ x - x) > w(x) + α}.

What is the terminology for these subgroups ? (I guess some variant of "ramification group of order α) ?
Can you indicate me a source ?
Thx.

2. Dec 24, 2014