通过普赖姆构造的 2∞ 塞尔默秩奇偶性

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory Pub Date : 2024-07-18 DOI:10.1016/j.jnt.2024.06.009

Jordan Docking

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引用次数: 0

摘要

我们推导出了一个 2 或 3 属曲线的雅各布秩的 2∞ 塞尔默秩奇偶性的局部公式。我们给出了一个明确的例子，说明这个局部公式如何给出秩奇偶性预测，从而可以检验2奇偶性猜想。我们的结果还应用于属 3 半稳曲线的奇偶性猜想。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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2∞-Selmer rank parities via the Prym construction

We derive a local formula for the parity of the $2^{\infty}$ -Selmer rank of Jacobians of curves of genus 2 or 3 which admit an unramified double cover. We give an explicit example to show how this local formula gives rank parity predictions against which the 2-parity conjecture may be tested. Our results yield applications to the parity conjecture for semistable curves of genus 3.

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来源期刊

Journal of Number Theory 数学-数学

CiteScore

1.30

自引率

14.30%

发文量

122

审稿时长

16 weeks

期刊介绍： The Journal of Number Theory (JNT) features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied areas. A valuable resource for mathematicians, the journal provides an international forum for the publication of original research in this field. The Journal of Number Theory is encouraging submissions of quality, long articles where most or all of the technical details are included. The journal now considers and welcomes also papers in Computational Number Theory. Starting in May 2019, JNT will have a new format with 3 sections: JNT Prime targets (possibly very long with complete proofs) high impact papers. Articles published in this section will be granted 1 year promotional open access. JNT General Section is for shorter papers. We particularly encourage submission from junior researchers. Every attempt will be made to expedite the review process for such submissions. Computational JNT . This section aims to provide a forum to disseminate contributions which make significant use of computer calculations to derive novel number theoretic results. There will be an online repository where supplementary codes and data can be stored.