Abstract
We establish Green equivalences for all Mackey 2-functors, without assuming Krull–Schmidt. By running through the examples of Mackey 2-functors, we recover all variants of the Green equivalence and Green correspondence known in representation theory and obtain new ones in several other contexts. Such applications include equivariant stable homotopy theory in topology and equivariant sheaves in geometry.
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Notes
We study cohomological Mackey 2-functors, in the above sense, in a separate article in preparation, where in particular we will justify the terminology ‘cohomological’.
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Communicated by Andreas Thom.
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Paul Balmer was supported by NSF Grant DMS-1901696. Ivo Dell’Ambrogio was supported by Project ANR ChroK (ANR-16-CE40-0003) and Labex CEMPI (ANR-11-LABX-0007-01).
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Balmer, P., Dell’Ambrogio, I. Green equivalences in equivariant mathematics. Math. Ann. 379, 1315–1342 (2021). https://doi.org/10.1007/s00208-021-02145-2
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DOI: https://doi.org/10.1007/s00208-021-02145-2