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The absolute Galois group $\Gal(\overline\Q/\Q)$ acts on the set of Artin representations for an extension by pre-composition, so we consider two representations to be Galois conjugate if they differ by such an automorphism. The action, for a given representation, in fact factors through a finite degree abelian extension.

The Galois orbit of a representation is its orbit under this action.

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• Review status: reviewed
• Last edited by Kiran S. Kedlaya on 2019-05-02 23:53:58
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