ℓ-torsion in class groups of certain families of D 4 -quartic fields
Chen An1
1 Department of Mathematics, Duke University 120 Science Drive, Durham, NC 27708, USA
Journal de théorie des nombres de Bordeaux, Volume 32 (2020) no. 1, pp. 1-23.

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.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/jtnb.1109
Classification: 11R29, 11R42, 11R45
Keywords: torsion, class group, Chebotarev density theorem

Chen An 1

1 Department of Mathematics, Duke University 120 Science Drive, Durham, NC 27708, USA
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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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, Volume 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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