Algebraic cycles and functorial lifts from G2 to PGSp6

IF 0.9 1区数学 Q2 MATHEMATICS

Algebra & Number Theory Pub Date : 2025-02-20 DOI:10.2140/ant.2025.19.551

Antonio Cauchi, Francesco Lemma, Joaquín Rodrigues Jacinto

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引用次数: 0

Abstract

We study instances of Beilinson–Tate conjectures for automorphic representations of ${PGSp}_{6}$ whose spin $L$ -function has a pole at $s = 1$ . We construct algebraic cycles of codimension 3 in the Siegel–Shimura variety of dimension 6 and we relate its regulator to the residue at $s = 1$ of the $L$ -function of certain cuspidal forms of ${PGSp}_{6}$ . Using the exceptional theta correspondence between the split group of type $G_{2}$ and ${PGSp}_{6}$ and assuming the nonvanishing of a certain archimedean integral, this allows us to confirm a conjecture of Gross and Savin on rank- $7$ motives of type $G_{2}$ .

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G2到PGSp6的代数环和函升

我们研究了自旋l函数在s= 1处有极点的PGSp的自同构表示的Beilinson-Tate猜想的实例。在6维的Siegel-Shimura变型中构造了余维数为3的代数环，并将其调节器与PGSp(6)的某些尖形l函数在s= 1处的残差联系起来。利用G2型分裂群与PGSp(6)之间的特殊对应关系，并假设某个阿基米德积分不消失，这使我们能够证实Gross和Savin关于G2型7阶动机的一个猜想。

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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来源期刊

Algebra & Number Theory MATHEMATICS-

CiteScore

1.80

自引率

7.70%

发文量

审稿时长

6-12 weeks

期刊介绍： ANT’s inclusive definition of algebra and number theory allows it to print research covering a wide range of subtopics, including algebraic and arithmetic geometry. ANT publishes high-quality articles of interest to a broad readership, at a level surpassing all but the top four or five mathematics journals. It exists in both print and electronic forms. The policies of ANT are set by the editorial board — a group of working mathematicians — rather than by a profit-oriented company, so they will remain friendly to mathematicians'' interests. In particular, they will promote broad dissemination, easy electronic access, and permissive use of content to the greatest extent compatible with survival of the journal. All electronic content becomes free and open access 5 years after publication.