The differential exponent can be computed from the orders of the higher ramification groups for Galois extensions:
2.
A sequence of ramification groups is defined, reifying ( amongst other things ) " wild " ( non-tame ) ramification.
3.
The ramification groups can be used to compute the different \ mathfrak { D } _ { L / K } of the extension L / K and that of subextensions:
4.
This allows one to define ramification groups in the upper numbering for infinite Galois extensions ( such as the absolute Galois group of a local field ) from the inverse system of ramification groups for finite subextensions.
5.
This allows one to define ramification groups in the upper numbering for infinite Galois extensions ( such as the absolute Galois group of a local field ) from the inverse system of ramification groups for finite subextensions.
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