Ramification groups #

The decomposition subgroup and inertia subgroups.

TODO: Define higher ramification groups in lower numbering


The decomposition subgroup defined as the stabilizer of the action on the type of all valuation subrings of the field.

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    The valuation subring A (considered as a subset of L) is stable under the action of the decomposition group.

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      The multiplicative action of the decomposition subgroup on A.

      The inertia subgroup defined as the kernel of the group homomorphism from the decomposition subgroup to the group of automorphisms of the residue field of A.

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