The system will be going down for regular maintenance. Please save your work and logout.
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
< Reduce
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Mathematical institute
Language
en
Communication dans un congrès
This item was published in
ANTS X - Tenth Algorithmic Number Theory Symposium, 2012-07-09, San Diego. 2013-11-14, vol. 1, p. 21-39
Mathematical Sciences Publisher
English 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 ...Read more >
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.Read less <
English Keywords
absolute Galois group
class field theory
group extensions
Origin
Hal imported