The absolute Galois group $\Gal(\overline\Q/\Q)$ acts on the set ofArtin representations for an extension by post-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.
- Review status: beta
- Last edited by John Jones on 2015-12-05 10:03:15