Let $A$ be a dvr with fraction field $K$ of characteristic zero. Let $L/K$ be a finite Galois extension and let $B$ be the integral closure of $A$ in $L$.
For a prime $b$ of $B$, let $e_b$ be its ramification index and $f_b$ its residue degree.
Do we have that $e_b$ and $f_b$ are independent of $b$?
I'm thinking about the topological point of view. When you have a topological covering $X\to X/G$ obtained by a free action of a finite group on a compact connected Riemann surface, you have that all ramification indices of points lying over a fixed point are equal.