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

Peter Koymans; Carlo Pagano

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

Number Theory 2021-03-09 v1

Authors: Peter Koymans , Carlo Pagano

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.

Keywords

multiquadratic fields class group 2-torsion sharp bound ray class group narrow class group ramifying primes

Cite

@article{arxiv.2009.08399,
  title  = {A sharp upper bound for the $2$-torsion of class groups of multiquadratic fields},
  author = {Peter Koymans and Carlo Pagano},
  journal= {arXiv preprint arXiv:2009.08399},
  year   = {2021}
}

Comments

Some of the results in this paper were originally part of arXiv:1909.13871, which is now split in two parts

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

Abstract

Keywords

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