论文标题
稳定模块的分解$ \ infty $ - 类别
Decompositions of the stable module $\infty$-category
论文作者
论文摘要
我们表明，有限组$ g $的稳定模块$ \ infty $ - 分类以三种不同的方式分解，作为稳定模块$ \ infty $ - $ g $的稳定模块$ \ infty $ - 类别。类似于Dwyer的同源性分解术语，我们称其为Centricerser，正常人和亚组分解。我们构建了Centryser和formoliser分解，并将亚组分解（由Mathew构建）扩展到更多亚组集合。证明的关键步骤是扩展为任何$ g $ - 空间定义的稳定模块$ \ infty $ - 类别，然后表明此扩展只取决于$ g $空加的$ s $ equivariant同型类型。所使用的方法不是特定于稳定模块$ \ infty $ - 类别的特定特定的，因此也可能适用于$ \ infty $ - 类别在$ g $上依赖的其他设置。
We show that the stable module $\infty$-category of a finite group $G$ decomposes in three different ways as a limit of the stable module $\infty$-categories of certain subgroups of $G$. Analogously to Dwyer's terminology for homology decompositions, we call these the centraliser, normaliser, and subgroup decompositions. We construct centraliser and normaliser decompositions and extend the subgroup decomposition (constructed by Mathew) to more collections of subgroups. The key step in the proof is extending the stable module $\infty$-category to be defined for any $G$-space, then showing that this extension only depends on the $S$-equivariant homotopy type of a $G$-space. The methods used are not specific to the stable module $\infty$-category, so may also be applicable in other settings where an $\infty$-category depends functorially on $G$.
