Top slope for a local field (reviewed)

Let $K$ be a $p$-adic field with slope content $[s_1, \ldots, s_k]_t^u$. The top slope refers to the ramification group $G^{(s)}$ with the largest $s$. So,

• if $k>0$, then the top slope is $s_k$, which is always greater than $1$
• otherwise, if $t>1$, then the top slope is $1$
• otherwise the top slope is $0$

This includes, by convention, that the top slope of $\Q_p$, as an extension of itself, is $0$.