How far is an extension of $p$-adic fields from having a normal integral basis?

Ilaria Del Corso, Fabio Ferri, Davide Lombardo

Let $L/K$ be a finite Galois extension of $p$-adic fields with group $G$. It is well-known that ${\mathcal{O}}_L$ contains a free ${\mathcal{O}}_K[G]$-submodule of finite index. We stu…