2020/02/26 by David Barnes, Barnes, David, Danny Sugrue +1
Mathematics · #Algebraic structures and combinatorial models #Advanced Algebra and Geometry #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2002.11745
For G a profinite group, we construct an equivalence between rational G-Mackey functors and a certain full subcategory of G-sheaves over the space of closed subgroups of G called Weyl-G-sheaves. This subcategory consists of those sheaves whose stalk over a subgroup K is K-fixed. This extends the classification of rational G-Mackey functors for finite G of Thévenaz and Webb, and Greenlees and May to a new class of examples. Moreover, this equivalence is instrumental in the classification of rational G-spectra for profinite G, as given in the second author's thesis.