mathlib documentation

ring_theory.valuation.ramification_group

Ramification groups #

The decomposition subgroup and inertia subgroups.

TODO: Define higher ramification groups in lower numbering

@[reducible]
def valuation_subring.decomposition_subgroup (K : Type u_1) {L : Type u_2} [field K] [field L] [algebra K L] (A : valuation_subring L) :

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 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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