Associated inertia (awaiting review)

Let $L/\Q_p$ be a finite extension, let $K$ be the maximal unramified subextension and let $\varphi \in K[x]$ be an Eisenstein polynomial defining $L/K$. The associated inertia of a segment of the ramification polygon of an $\varphi$ is the least common multiple of the degrees of the irreducible factors of the residual polynomial of that segment. The associated inertias are divisors of the inertia degree of $\varphi$ and are invariants of $L$.