Categories of modules for profinite groups.

有限组的模块类别。

• 批准号: 2861690
• 金额: --
• 依托单位: University of Manchester
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2022
• 资助国家: 英国
• 起止时间: 2022 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2861690
• 关键词: Categories; modules; profinite; groups.

A long-established method of studying a group is to study its modules. This is most developed in the case of finite groups, but modules are also studied for infinite groups and it is now well understood that a great deal of information can be obtained by studying various categories of these modules and their subcategories. For a topological group, the topology must be taken into account and it is not entirely clear which are the best types of modules to study. This project concerns the specific case of profinite groups, which are infinite groups but with a topology that often gives them properties similar to those of finite groups. It aims to set up a categorical framework for modules for profinite groups that parallels that for discrete infinite groups. The project lies within the EPSRC research area of Algebra.

研究一个群体的一个长期建立的方法是研究它的模块。这是最发达的情况下，有限的群体，但模也研究了无限的群体，现在很好地理解，大量的信息可以获得通过研究各种类别的这些模块及其子类别。对于一个拓扑群，必须考虑拓扑结构，并且还不完全清楚哪些是最好的模类型。这个项目关注profinite群的具体情况，profinite群是无限群，但其拓扑结构通常赋予它们与有限群相似的性质。它的目的是建立一个范畴的框架模profinite群平行的离散无限群。该项目属于EPSRC代数研究领域。