Local field invariants (reviewed)

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 $\textrm{Aut}(K/\mathbb Q_p)$.