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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 $\rho$.

Knowl status:
  • Review status: reviewed
  • Last edited by Alina Bucur on 2019-05-02 21:25:59
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