A sharp upper bound for the 2-torsion of class groups of multiquadratic fields

Koymans, Peter; Pagano, Carlo

doi:10.1112/mtk.12123

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A sharp upper bound for the 2-torsion of class groups of multiquadratic fields

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Koymans, Peter
Max Planck Institute for Mathematics, Max Planck Society;

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Pagano, Carlo
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1112/mtk.12123
(Publisher version)

https://doi.org/10.48550/arXiv.2009.08399
(Preprint)

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Koymans-Pagano_A sharp upper bound for the 2-torsion of class groups of multiquadratic fields_2022.pdf
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Citation

Koymans, P., & Pagano, C. (2022). A sharp upper bound for the 2-torsion of class groups of multiquadratic fields. Mathematika, 68(1), 237-258. doi:10.1112/mtk.12123.

Cite as: https://hdl.handle.net/21.11116/0000-000A-39EC-D

Abstract

Let $K$ be a multiquadratic extension of $\mathbb{Q}$ and let
$\text{Cl}^{+}(K)$ be its narrow class group. Recently, the authors \cite{KP}
gave a bound for $|\text{Cl}^{+}(K)[2]|$ only in terms of the degree of $K$ and
the number of ramifying primes. In the present work we show that this bound is
sharp in a wide number of cases. Furthermore, we extend this to ray class
groups.