Equivariant sheaves for profinite groups

Barnes, David; Sugrue, Danny

doi:10.1016/j.topol.2022.108215

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•4 Equivariant Sheaves1

•1 Examples1

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2022

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“…We begin with the definition of a G-equivariant sheaf over a profinite G-space X where G is a profinite group. The second author gives two equivalent definitions in [Sug19], see also [BS20]. We work with just one for brevity.…”

Section: •4 Equivariant Sheavesmentioning

confidence: 99%

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

Barnes¹,

Sugrue²

2022

Math. Proc. Camb. Phil. Soc.

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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.

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Section: •4 Equivariant Sheavesmentioning

confidence: 99%

“…Just as non-equivariantly, one can make constant sheaves and skyscraper sheaves. We leave the details to the second author's thesis [Sug19] and the forthcoming paper by the authors [BS20]. The stalks of the constant sheaf at a Q-module B are all isomorphic to B.…”

Section: •1 Examplesmentioning

confidence: 99%