FROM PICARD GROUPS OF HYPERELLIPTIC CURVES TO CLASS GROUPS OF QUADRATIC FIELDS

被引：2

作者：

Gillibert, Jean ^{[1
]}

机构：

[1] Inst Math Toulouse, CNRS, UMR 5219, 118 Route Narbonne, F-31062 Toulouse 9, France

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2021年 / 374卷 / 06期

关键词：

LINE BUNDLES;

D O I：

10.1090/tran/8334

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let C be a hyperelliptic curve defined over Q, whose Weierstrass points are defined over extensions of 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.

引用

页码：3919 / 3946

页数：28

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