The Picard group in equivariant homotopy theory via stable module categories

2020/08/12 by Achim Krause, Krause, Achim · 3 citations
Mathematics · Physics and Astronomy · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics

paper · pdf · doi:10.48550/arxiv.2008.05551

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=A₅. A further application is given by showing that the Picard groups of Sp^G and a category of derived Mackey functors agree.

Citations

• Nilpotence and descent in equivariant stable homotopy theory
• On the nonexistence of elements of Kervaire invariant one
• On topological cyclic homology
• The spectrum of derived Mackey functors

Cited by

• Duality in tensor-triangular geometry via proxy-smallness
• Semifree Isovariant Poincaré Spaces and the Gap Condition
• Stratifying integral representations of finite groups

Related

• Picard Groups in Equivariant Algebra and Stable Homotopy Theory
• Homotopy Representations and the Picard Group of the Equivariant Stable Homotopy Category
• The Picard group of the category of C_n-equivariant stable homotopy theory
• Modular fixed points in equivariant homotopy theory
• Rigidity and exotic models for v₁-local G-equivariant stable homotopy theory