Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Ramification group of valuations - need terminology

  1. Dec 19, 2014 #1
    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 ?
  2. jcsd
  3. Dec 24, 2014 #2
    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?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Ramification group valuations Date
I Correspondence Theorem for Groups ... Another Question ... Today at 5:01 AM
I Correspondence Theorem for Groups ... Rotman, Propn 1.82 ... Yesterday at 9:32 PM
I Lorentz Group Mar 14, 2018
A Why a Lie Group is closed in GL(n,C)? Feb 12, 2018
P-adic norm, valuation, and expansion Feb 25, 2015