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An Artin representation is a continuous homomorphism $\rho:\mathrm{Gal}(\overline{\Q}/\Q)\to\GL(V)$ from the absolute Galois group of $\Q$ to the automorphism group of a finite-dimensional $\C$-vector space $V$. Here continuity means that $\rho$ factors through the Galois group of some finite extension $K/\Q$. The smallest such $K$ is called the Artin field of $\rho$.

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• Last edited by Andrew Sutherland on 2019-07-31 15:05:06
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