Family labels (awaiting review)

Let $K$ be a finite extension of $\Q_p$, with $K\ne\Q_p$. The label associated to a relative family $I/K$ has the form $s\text{-}f.e.c\ell$, where

• $s$ is the label attached to the base field $K$,
• $f$ is the residue field degree of every $L/K\in I/K$,
• $e$ is the ramification index of every $L/K\in I/K$,
• $c$ is the discriminant exponent of every $L/K\in I/K$,
• $\ell$ is a string of one or more letters used to distinguish families with the same basic data. It is defined by sorting the families by their number of wild segments, then the list of lengths of the wild segments, then the rams.

The label associated to an absolute family $I/\Q_p$ has the form $p.f.e.c\ell$, where $f,e,c,\ell$ are defined as above, with $K=\Q_p$.