Is there a definition out there of the notion of conductor of a non-abelian number field? If not, is there anyone you know of working on it? The definition for abelian number fields uses class field theory; it comes out of Artin reciprocity.

Is there a definition out there of the notion of conductor of a non-abelian number field (i.e. a finite extension of Q whose Galois group is non-abelian)? If not, is there anyone you know of working on it? The definition for abelian number fields uses class field theory; it comes out of Artin reciprocity (see page 525 of Neukirch's Algebraic number theory).