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arXiv · 2002.11745

The equivalence between rational G-sheaves and rational G-Mackey functors for profinite G

David Barnes·Danny Sugrue
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Abstract

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 Th\'{e}venaz 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.

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David Barnes, Danny Sugrue. 2020-02-26. The equivalence between rational G-sheaves and rational G-Mackey functors for profinite G. https://arxiv.org/abs/2002.11745

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