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On the p-rank of the class group of quadratic number fields

Helminck, P.A. (2014) On the p-rank of the class group of quadratic number fields. Master's Thesis / Essay, Mathematics.

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Abstract

The main goal of this thesis is to obtain quadratic number fields such that the p-rank of the class group is high. This is done by geometric means, more specifically: elliptic curves with p-torsion are used. To obtain a high p-rank, we use Jacobians that decompose into at least two elliptic curves, each of which having an isogeny of degree p to it. Several constructions of such Jacobians are given. Also, the influence of the rank of an elliptic curve on the p-rank of the class group is shown.

Item Type: Thesis (Master's Thesis / Essay)
Degree programme: Mathematics
Thesis type: Master's Thesis / Essay
Language: English
Date Deposited: 15 Feb 2018 07:58
Last Modified: 15 Feb 2018 07:58
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/12174

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