Annihilators of minus class groups of imaginary abelian fields

Greither, Cornelius; Kučera, Radan

doi:10.5802/aif.2309

Annihilators of minus class groups of imaginary abelian fields
[Annulateurs pour la partie moins du groupe des classes d’un corps abélien imaginaire]

Greither, Cornelius ¹ ; Kučera, Radan ²

¹ Universität der Bundeswehr München Fakultät für Informatik Institut für theoretische Informatik und Mathematik 85577 Neubiberg (Germany)
² Masarykova univerzita Přírodovědecká fakulta Janáčkovo nám. 2a 602 00 Brno (Czech Republic)

Annales de l'Institut Fourier, Tome 57 (2007) no. 5, pp. 1623-1653.

Résumé
Abstract

Pour certains corps imaginaires abéliens, on trouve des annulateurs pour la partie moins du groupe des classes en dehors de l’idéal de Stickelberger. En fonction du cadre précis, on emploie des méthodes différentes. Les résultats théoriques sont accompagnés de calculs numériques, ayant trait à quelques cas extrêmes.

For certain imaginary abelian fields we find annihilators of the minus part of the class group outside the Stickelberger ideal. Depending on the exact situation, we use different techniques to do this. Our theoretical results are complemented by numerical calculations concerning borderline cases.

MR Zbl

DOI : 10.5802/aif.2309

Classification : 11R20, 11R29
Keywords: Imaginary abelian number fields, minus part of the ideal class group, annihilators, Stickelberger ideal, Fitting ideals
Mot clés : corps de nombres abéliens imaginaires, partie moins du groupe des classes, annulateurs, idéal de Stickelberger, idéaux de Fitting

Affiliations des auteurs :

Greither, Cornelius ¹ ; Kučera, Radan ²

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Greither, Cornelius; Kučera, Radan. Annihilators of minus class groups of imaginary abelian fields. Annales de l'Institut Fourier, Tome 57 (2007) no. 5, pp. 1623-1653. doi : 10.5802/aif.2309. http://www.numdam.org/articles/10.5802/aif.2309/

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