Connected abelian complex Lie groups and number fields
Vallières, Daniel1
1 University of California, San Diego 9500 Gilman Drive # 0112 La Jolla, CA 92093-0112 USA Current address : Fakultät für Mathematik Institut für theoritische Informatik und Mathematik Universität der Bundeswehr Münschen 85577 Neubiberg Deutschland
Journal de théorie des nombres de Bordeaux, Tome 24 (2012) no. 1, pp. 201-229.

Dans cet article, nous expliquons une façon d’associer à tout corps de nombres certains groupes de Lie complexes et connexes. Nous étudions en particulier le cas des corps de nombres de degré 3 sur ℚ qui ne sont pas totalement réels et expliquons le lien entre ceux-ci et les groupes de Cousin (“groupes toroidaux”) de dimension complexe 2 et de rang 3.

In this note we explain a way to associate to any number field some connected complex abelian Lie groups. Further, we study the case of non-totally real cubic number fields, and we see that they are intimately related with the Cousin groups (toroidal groups) of complex dimension 2 and rank 3.

DOI : 10.5802/jtnb.793
Vallières, Daniel 1

1 University of California, San Diego 9500 Gilman Drive # 0112 La Jolla, CA 92093-0112 USA Current address : Fakultät für Mathematik Institut für theoritische Informatik und Mathematik Universität der Bundeswehr Münschen 85577 Neubiberg Deutschland 
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Vallières, Daniel. Connected abelian complex Lie groups and number fields. Journal de théorie des nombres de Bordeaux, Tome 24 (2012) no. 1, pp. 201-229. doi : 10.5802/jtnb.793. https://www.numdam.org/articles/10.5802/jtnb.793/

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