论 CM 环状体的玉川数

IF 0.9 1区数学 Q2 MATHEMATICS

Algebra & Number Theory Pub Date : 2024-02-16 DOI:10.2140/ant.2024.18.583

Pei-Xin Liang, Yasuhiro Oki, Hsin-Yi Yang, Chia-Fu Yu

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引用次数: 0

摘要

我们研究了计算 CM 索的玉川数问题。这个问题自然产生于阿赫特、阿尔图格、加西亚和戈登，以及郭、谢和余等人分别在有限域上计算具有交换内态群的极化无性变数，以及极化 CM 无性变数和单元志村变数成分的问题。我们对更一般背景下的伽罗瓦同调群进行了系统研究，并计算了与各种伽罗瓦 CM 场相关的 CM 转矩的玉川数。此外，我们证明了 2 的每一个（正或负）幂都是 CM tori 的玉川数，证明了小野对 CM tori 的类似猜想。

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On Tamagawa numbers of CM tori

We investigate the problem of computing Tamagawa numbers of CM tori. This problem arises naturally from the problem of counting polarized abelian varieties with commutative endomorphism algebras over finite fields, and polarized CM abelian varieties and components of unitary Shimura varieties in the works of Achter, Altug, Garcia and Gordon and of Guo, Sheu and Yu, respectively. We make a systematic study on Galois cohomology groups in a more general setting and compute the Tamagawa numbers of CM tori associated to various Galois CM fields. Furthermore, we show that every (positive or negative) power of $2$ is the Tamagawa number of a CM tori, proving the analogous conjecture of Ono for CM tori.

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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.