Wild Ramification

Ramification in an extension of local or global fields at a prime where the ramification index is divisible by the residue characteristic p, producing nontrivial higher ramification groups and more complicated arithmetic and Galois-module structure than the tame case.

Ramification occurring in arithmetic or algebraic extensions when higher ramification groups are nontrivial in residue characteristic p dividing the ramification index, producing more complicated, higher-order behaviour than the tame case.