  Given a hilbertian field $k$ of characteristic zero and a finite Galois
extension $E/k(T)$ with group $G$ such that $E/k$ is regular, we produce some
specializations of $E/k(T)$ at points $t_0 \in \mathbb{P}^1(k)$ which have the
same Galois group but also specified inertia groups at finitely many given
primes. This result has two main applications. Firstly we conjoin it with
previous works to obtain Galois extensions of $\mathbb{Q}$ of various finite
groups with specified local behavior - ramified or unramified - at finitely
many given primes. Secondly, in the case $k$ is a number field, we provide
criteria for the extension $E/k(T)$ to satisfy this property: at least one
Galois extension $F/k$ of group $G$ is not a specialization of $E/k(T)$.
