Ramification group

Summary

The ramification groups of a finite Galois extension of local fields form a decreasing chain of normal subgroups $G_0 \supseteq G_1 \supseteq G_2 \supseteq \cdots$ of its Galois group. The group $G_0$ is the inertia group, and $G_1$ is the wild inertia group. The chain measures how deeply the extension is ramified. It controls the different and the conductor of the extension.