Ramified prime of an Artin representation (reviewed)

If $\rho:\Gal(\overline\Q/\Q)\to\GL_n(\C)$ is an Artin representation with Artin field $K$, then a prime $p$ is ramified if it is ramified in $K/\Q$.

Equivalently, a prime is ramified if the inertia subgroup for a prime above $p$ is not contained in the kernel of $\rho$.