Rational G-spectra over blocks with finite Weyl groups

2025/08/11 by J. P. C. Greenlees, Greenlees, J. P. C.
Mathematics · #55N91 #55P42 #55P62 #55P91 #55Q45 #55Q91 #Advanced Algebra and Geometry #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2508.07752

openalex publication_date 2025/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that for any clopen collection X of subgroups of G with finite Weyl groups, the category of G-spectra with geometric isotropy in X is equivalent to the category of equivariant sheaves over X. This gives an algebraic model of injective dimension at most the rank of G.

Citations

• Rational SU(3)-equivariant cohomology theories
• An algebraic model for rational U(2)-spectra
• Rational G-spectra for rank 2 toral groups of mixed type
• Algebraic models for 1-dimensional categories of rational G-spectra
• Spaces of subgroups of toral groups
• Prismatic decompositions and rational G-spectra
• Separated and complete adelic models for one-dimensional Noetherian tensor-triangulated categories
• Equivariant sheaves for profinite groups
• Adelic models of tensor-triangulated categories
• Adelic cohomology
• Homotopy theory of modules over diagrams of rings
• Rational O(2)-Equivariant Spectra

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• Algebraic models for 1-dimensional categories of rational G-spectra
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• An introduction to algebraic models for rational G-spectra