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 $0$.

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**Knowl status:**

- Review status: reviewed
- Last edited by Andrew Sutherland on 2020-10-24 17:13:57

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**History:**(expand/hide all)

- 2020-10-24 17:13:57 by Andrew Sutherland (Reviewed)
- 2018-05-23 15:09:47 by John Cremona (Reviewed)

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