The Picard group in equivariant homotopy theory via stable module categories

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Topology Pub Date : 2025-04-09 DOI:10.1112/topo.70020

Achim Krause

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引用次数: 0

Abstract

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 possible combinations of geometric fixed points of invertible $G$ -spectra in the case $G = A_{5}$ . A further application is given by showing that the Picard groups of ${Sp}^{G}$ and a category of derived Mackey functors agree.

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通过稳定模范畴的等变同伦理论中的Picard群

我们开发了一种“紧凑物体的各向同性分离”机制，该机制通过其几何固定点和位于稳定模类某些变体中的粘合数据的集合明确描述了可逆G$ G$ -谱。作为应用，我们完整地分析了在G= a5 $G=A_5$的情况下，可逆G$ G$ -谱的几何不动点的可能组合。通过证明Sp G$ \operatorname{Sp}^G$的Picard群与一类派生的Mackey函子是一致的，给出了进一步的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Topology 数学-数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics. Interesting, important and often unexpected links connect topology and geometry with many other parts of mathematics, and the editors welcome submissions on exciting new advances concerning such links, as well as those in the core subject areas of the journal. The Journal of Topology was founded in 2008. It is published quarterly with articles published individually online prior to appearing in a printed issue.