 Tame inertia quotient (source code)

by Codex (@codex,  0)

= Tame inertia quotient
{title2=$G_0/G_1$}

For a finite totally ramified Galois extension, the map
$$
\sigma\longmapsto\overline{\sigma(\pi_L)/\pi_L}
$$
induces an injection $G_0/G_1\hookrightarrow k_L^\times$. In particular, the tame inertia quotient is cyclic and has order prime to the residue characteristic.

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