$\ell $-torsion in class groups of certain families of $D_4$-quartic fields

Chen An

doi:10.5802/jtnb.1109

ℓ

-torsion in class groups of certain families of

D_{4}

-quartic fields

Chen An ¹

¹ Department of Mathematics, Duke University 120 Science Drive, Durham, NC 27708, USA

Journal de théorie des nombres de Bordeaux, Tome 32 (2020) no. 1, pp. 1-23.

Résumé
Abstract

Nous donnons une borne supérieure pour la $ℓ$ -torsion des groupes de classes pour presque tous les corps de certaines familles des corps quartiques de type $D_{4} .$ Nos outils principaux sont une nouvelle version du théorème de densité de Chebotarev pour ces familles et une borne inférieure sur le nombre de corps dans les familles.

We prove an upper bound for $ℓ$ -torsion in class groups of almost all fields in certain families of $D_{4}$ -quartic fields. Our key tools are a new Chebotarev density theorem for these families of $D_{4}$ -quartic fields and a lower bound for the number of fields in the families.

Reçu le : 2018-08-07
Révisé le : 2019-12-06
Accepté le : 2019-12-22
Publié le : 2020-08-21

DOI : 10.5802/jtnb.1109

Classification : 11R29, 11R42, 11R45
Mots clés : torsion, class group, Chebotarev density theorem

Affiliations des auteurs :

Chen An ¹

¹ Department of Mathematics, Duke University 120 Science Drive, Durham, NC 27708, USA

Licence :

CC-BY-ND 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {$\ell $-torsion in class groups of certain families of $D_4$-quartic fields},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {1--23},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {32},
     number = {1},
     year = {2020},
     doi = {10.5802/jtnb.1109},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1109/}
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Chen An. $\ell $-torsion in class groups of certain families of $D_4$-quartic fields. Journal de théorie des nombres de Bordeaux, Tome 32 (2020) no. 1, pp. 1-23. doi : 10.5802/jtnb.1109. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1109/

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