An explicit family of cubic number fields with large $2$-rank of the class group

Avinash Kulkarni

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arXiv · 1610.07668

An explicit family of cubic number fields with large $2$-rank of the class group

Avinash Kulkarni

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Abstract

We show how to construct infinite families of explicitly determined cubic number fields whose class group has a subgroup isomorphic to $(\mathbb{Z}/2)^8$ using degree $1$ del Pezzo surfaces. We illustrate the method and provide an example of such a family.

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Avinash Kulkarni. 2016-10-24. An explicit family of cubic number fields with large $2$-rank of the class group. https://arxiv.org/abs/1610.07668

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