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arXiv · 1807.02823

From Picard groups of hyperelliptic curves to class groups of quadratic fields

Jean Gillibert
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Abstract

Let $C$ be a hyperelliptic curve defined over $\mathbb{Q}$, whose Weierstrass points are defined over extensions of $\mathbb{Q}$ of degree at most three, and at least one of them is rational. Generalizing a result of R. Soleng (in the case of elliptic curves), we prove that any line bundle of degree $0$ on $C$ which is not torsion can be specialised into ideal classes of imaginary quadratic fields whose order can be made arbitrarily large. This gives a positive answer, for such curves, to a question by Agboola and Pappas.

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Jean Gillibert. 2018-07-08. From Picard groups of hyperelliptic curves to class groups of quadratic fields. https://arxiv.org/abs/1807.02823

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