$\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.

Abstract (VO)
Résumé

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.

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.

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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     author = {Chen An},
     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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