Enumeration of Isomorphism Classes of Extensions of p-adic Fields

Xiang-dong Hou, Kevin Keating

Let $\Omega$ be an algebraic closure of ${\mathbb{Q}}_p$ and let $F$ be a finite extension of ${\mathbb{Q}}_p$ contained in $\Omega$. Given positive integers $f$ and $e$, the number of extensi…