计算有限域上两条椭圆曲线乘积的布劳尔群

IF 0.7 4区数学 Q3 MATHEMATICS, APPLIED

Japan Journal of Industrial and Applied Mathematics Pub Date : 2023-12-28 DOI:10.1007/s13160-023-00638-y

Akira Katayama, Masaya Yasuda

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引用次数: 0

摘要

我们讨论如何计算有限域上两条椭圆曲线乘积的布劳尔群。具体来说，我们应用无性曲面的阿尔丁-塔特公式，给出了计算两条椭圆曲线乘积的布劳尔群阶数的简单公式。我们的公式可以利用椭圆曲线上弗罗贝尼斯映射的迹和两个椭圆曲线之间同态群的判别式来计算布劳尔群的阶。此外，对于非同源椭圆曲线的乘积，我们给出了一种算法，用于计算某个伽罗瓦同调的扭转子群，这些扭转子群可以嵌入为布劳尔群的子群。

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Computing the Brauer group of the product of two elliptic curves over a finite field

We discuss how to compute the Brauer group of the product of two elliptic curves over a finite field. Specifically, we apply the Artin–Tate formula for abelian surfaces to give a simple formula for computing the order of the Brauer group of the product of two elliptic curves. Our formula enables to compute the order of the Brauer group using traces of Frobenius maps on elliptic curves and the discriminant of the group of homomorphisms between two elliptic curves. In addition, for the product of non-isogenous elliptic curves, we give an algorithm for computing torsion subgroups of a certain Galois cohomology that can be embedded as subgroups of the Brauer group.

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来源期刊

Japan Journal of Industrial and Applied Mathematics 数学-应用数学

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： Japan Journal of Industrial and Applied Mathematics (JJIAM) is intended to provide an international forum for the expression of new ideas, as well as a site for the presentation of original research in various fields of the mathematical sciences. Consequently the most welcome types of articles are those which provide new insights into and methods for mathematical structures of various phenomena in the natural, social and industrial sciences, those which link real-world phenomena and mathematics through modeling and analysis, and those which impact the development of the mathematical sciences. The scope of the journal covers applied mathematical analysis, computational techniques and industrial mathematics.