Ramification group of valuations - need terminology

  • #1
200
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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.
 

Answers and Replies

  • #2
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Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 

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