mathlib documentation


Ramification groups #

The decomposition subgroup and inertia subgroups.

TODO: Define higher ramification groups in lower numbering

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.


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


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.