Theta 循环和贝林松-布洛赫-卡托猜想

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory Pub Date : 2024-05-06 DOI:10.1016/j.jnt.2024.04.001

Daniel Disegni

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引用次数: 0

摘要

我们在某些具有共轭交错对称性的伽罗瓦表示的塞尔默群中引入了 "典型 "类。它们是单元志村变中特殊循环的图像，并且是唯一定义的标量。这一构造是对刘玉良的构造的细微改进，它基于库德拉特殊循环的 Theta 序列的猜想模块性。对于二维表示，Theta 循环是（希格纳点的塞尔玛图像）。一般而言，它们在秩 1 中与贝林森-布洛赫-加藤猜想有类似的紧密联系，我们收集了这方面的现有证据。

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Theta cycles and the Beilinson–Bloch–Kato conjectures

We introduce ‘canonical’ classes in the Selmer groups of certain Galois representations with a conjugate-symplectic symmetry. They are images of special cycles in unitary Shimura varieties, and defined uniquely up to a scalar. The construction is a slight refinement of one of Y. Liu, based on the conjectural modularity of Kudla's theta series of special cycles. For 2-dimensional representations, Theta cycles are (the Selmer images of) Heegner points. In general, they conjecturally exhibit an analogous strong relation with the Beilinson–Bloch–Kato conjectures in rank 1, for which we gather the available evidence.

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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.