On norm residue symbols and conductors

Abstract

Using the norm residue symbol and a reciprocity law of Artin and Hasse, we determine the conductors of Kummer extensions of the form K(a, ζn)/K(ζn) for any unramified extension K of Qp, element a∈K*, and primitive pnth root of unity ζn. We are able to do this without more recent and general reciprocity laws, which were needed in earlier proofs of the case K=Qp. © 2001 Academic Press.