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arXiv · 2008.05551

The Picard group in equivariant homotopy theory via stable module categories

Achim Krause
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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 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.

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Achim Krause. 2020-08-12. The Picard group in equivariant homotopy theory via stable module categories. https://arxiv.org/abs/2008.05551

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