Year: 2013
Type: article
Abstract: In 1976, Onabe discovered that, in contrast to the Neukirch-Uchida results that were proved around the same time, a number field K is not completely characterized by its absolute abelian Galois group A K .The first examples of nonisomorphic K having isomorphic A K were obtained on the basis of a classification by Kubota of idele class character groups in terms of their infinite families of Ulm invariants, and did not yield a description of A K .In this paper, we provide a direct "computation" of the profinite group A K for imaginary quadratic K, and use it to obtain many different K that all have the same minimal absolute abelian Galois group.
Source: The Open Book Series
Authors: Athanasios Angelakis, Peter Stevenhagen
Institutions: Leiden University, Institut de Mathématiques de Bordeaux
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W2950189216