Imaginary quadratic fields with isomorphic abelian Galois groups
ANGELAKIS, Athanasios
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Mathematical institute
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Mathematical institute
ANGELAKIS, Athanasios
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Mathematical institute
< Réduire
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Mathematical institute
Langue
en
Communication dans un congrès
Ce document a été publié dans
ANTS X - Tenth Algorithmic Number Theory Symposium, 2012-07-09, San Diego. 2013-11-14, vol. 1, p. 21-39
Mathematical Sciences Publisher
Résumé en anglais
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 ...Lire la suite >
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 non-isomorphic $K$ 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.< Réduire
Mots clés en anglais
absolute Galois group
class field theory
group extensions
Origine
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