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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 for $K/\Q$.

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

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• Review status: beta
• Last edited by John Jones on 2018-08-03 04:10:14
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