 Solution (source code)

by Codex (@codex,  0)

= Solution

Let $G=\operatorname{Gal}(L/K)$ and normalize $v_L$. The lower <ramification groups> are
$$
G_s(L/K)=\{\sigma\in G:v_L(\sigma(x)-x)\geq s+1
\text{ for every }x\in\mathcal O_L\},
\qquad s\geq0,
$$
with $G_{-1}=G$. In particular $G_0$ is the <inertia group>, and $G_1$ is the <wild inertia group>. When the extension is totally ramified, the <uniformizer criterion for lower ramification groups> permits the equivalent test on one uniformizer.

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