标题： 等变同伦论中的模固定点 显示英文标题

标题： Modular fixed points in equivariant homotopy theory

摘要： 我们证明了置换模的导出$\infty$-范畴与等变谱在$\infty$-范畴中由常Mackey函子关联的Eilenberg-MacLane谱上的模范畴是等价的。 在这样的模范畴上，我们通过几何固定点再进行标量扩展来定义一个模固定点函子，并将其与Balmer-Gallauer引入的导出置换模上的模固定点函子相联系。 作为应用，我们证明了对于一个$p$-群，此类模范畴的Picard群由满足Borel-Smith条件的类函数构成。 在表示论的语言中，这个结果最早由Miller得到。 显示英文摘要

摘要： We show that the derived $\infty$-category of permutation modules is equivalent to the category of modules over the Eilenberg-MacLane spectrum associated to a constant Mackey functor in the $\infty$-category of equivariant spectra. On such module categories we define a modular fixed point functor using geometric fixed points followed by an extension of scalars and identify it with the modular fixed point functor on derived permutation modules introduced by Balmer-Gallauer. As an application, we show that the Picard group of such a module category for a $p$-group is given by the group of class functions satisfying the Borel-Smith conditions. In the language of representation theory, this result was first obtained by Miller.