We discuss the eld-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).
Cite this article
Yuichiro Hoshi, On the Field-theoreticity of Homomorphisms between the Multiplicative Groups of Number Fields. Publ. Res. Inst. Math. Sci. 50 (2014), no. 2, pp. 269–285DOI 10.4171/PRIMS/133