Number fields whose Abelian closures have isomorphic Galois groups
Résumé
Following a paper by Athanasios Angelakis and Peter Stevenhagen on the determination of imaginary quadratic fields having the same absolute Abelian Galois group (arXiv:1209.6005), we study this property for arbitrary number fields. We show that such a property is probably not generalizable to fields not imaginary quadratic, because of some p-adic obstructions about the units. By restriction to the p-parts of the Galois groups, we show that the corresponding study is related to the classical notion of p-rational fields. All this is a consequence of results yet published in our Springer book on class field theory.
Domaines
Théorie des nombres [math.NT]
Origine : Fichiers produits par l'(les) auteur(s)