Green equivalences in equivariant mathematics
arXiv:2001.10646 · doi:10.1007/s00208-021-02145-2
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.
25 pages. References updated, final version. To appear in Math. Ann