Solution

Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 29 / 4 / a / Solution

Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 24 / 5 / a / Solution

{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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