I'm looking for a "simple" proof of the fact that all ramified primes divides the conductor of an extension.
By "simple" i mean a proof which DOES'NT use local Artin map, norm residue symbol etc (as in Bochéat-Mischler, Janusz, Neukirsch) I don't need deeper results for example about the exponents; just the fact that ramified primes divides the conductors.
I would be very astonished if this result wasn't well known before Artin.