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arXiv · 2009.08399

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

Peter Koymans·Carlo Pagano
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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.

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Peter Koymans, Carlo Pagano. 2020-09-17. A sharp upper bound for the $2$-torsion of class groups of multiquadratic fields. https://arxiv.org/abs/2009.08399

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