On the Field-theoreticity of Homomorphisms between the Multiplicative Groups of Number Fields

Abstract

We discuss the field-theoreticity of homomorphisms between the multiplicative groups of number fields. We prove that, for instance, for a given isomorphism between the multiplicative groups of number fields, either the isomorphism or its multiplicative inverse arises from an isomorphism of fields if and only if the given isomorphism is SPU-preserving (i.e., roughly speaking, preserves the subgroups of principal units with respect to various nonarchimedean primes).