Cohomology of arithmetic groups in GL(2) over definite quaternion algebras

GL(2) 定四元数代数上算术群的上同调

• 批准号: 2884658
• 金额: --
• 依托单位: University of Sheffield
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2023
• 资助国家: 英国
• 起止时间: 2023 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2884658
• 关键词: Cohomology; arithmetic; groups; GL; over

In this project, we will explore the cohomology of arithmetic groups arising from 2-by-2 matrices with entries coming from orders in definite quaternion algebras over the rational numbers. Such arithmetic groups give natural generalisations of the Bianchi groups and they act as isometries of hyperbolic 5-space. We will develop computer programs that will compute the cohomology of such arithmetic groups together with the action of Hecke operators. We will use these programs to explore various open conjectures that lie at the forefront of modern number theory.

在这个项目中，我们将探索由 2×2 矩阵产生的算术群的上同调，该矩阵的条目来自有理数上的定四元数代数的阶。这样的算术群给出了 Bianchi 群的自然推广，并且它们充当双曲 5 空间的等距。我们将开发计算机程序来计算此类算术群的上同调以及赫克算子的作用。我们将使用这些程序来探索现代数论前沿的各种开放猜想。