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

Volume 182 / 2018

Avinash Kulkarni Acta Arithmetica 182 (2018), 117-132 MSC: Primary 11R29; Secondary 11G30, 14J26. DOI: 10.4064/aa8669-10-2017 Published online: 28 December 2017

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.

Authors

  • Avinash KulkarniDepartment of Mathematics
    Simon Fraser University
    Burnaby, BC, Canada, V5A 1S6
    e-mail

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