The basic invariants of a $p$-adic field $K$ are:

- the residue field characteristic $p$,
- the degree $d$,
- the ramification index $e$,
- the residue field degree $f$.
- the discriminant exponent $c$,
- the discriminant root field $\mathbb Q_p(\sqrt{\textrm{disc}(K)})$,
- the root number $\varepsilon$,
- the automorphism group $\textrm{Aut}(K/\mathbb Q_p)$.

**Knowl status:**

- Review status: reviewed
- Last edited by Andrew Sutherland on 2020-10-24 17:08:50

**Referred to by:**

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

- 2020-10-24 17:08:50 by Andrew Sutherland (Reviewed)
- 2020-10-24 16:45:03 by Andrew Sutherland
- 2020-10-24 16:44:23 by Andrew Sutherland
- 2018-05-23 14:58:44 by John Cremona (Reviewed)

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