论文标题
PICARD组在稳定模块类别中
The Picard group in equivariant homotopy theory via stable module categories
论文作者
论文摘要
我们开发了一种“紧凑对象的各向同性分离”的机制，该机制通过其在稳定模块类别的某些变体中的几何固定点和粘合数据收集来明确描述可逆的$ g $ spectrum。作为一个应用程序，我们在情况下对可逆的G-spectra进行了完整的分析。$ g = a_5 $。通过证明$ \ mathrm {sp}^g $的PICARD组和派生的Mackey Foundors同意的类别来给出进一步的应用程序。
We develop a mechanism of "isotropy separation for compact objects" that explicitly describes an invertible $G$-spectrum through its collection of geometric fixed points and gluing data located in certain variants of the stable module category. As an application, we carry out a complete analysis of invertible G-spectra in the case $G=A_5$. A further application is given by showing that the Picard groups of $\mathrm{Sp}^G$ and a category of derived Mackey functors agree.
