Green equivalences in equivariant mathematics
Abstract
We establish Green equivalences for all Mackey 2functors, without assuming KrullSchmidt. By running through the examples of Mackey 2functors, 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.
 Publication:

arXiv eprints
 Pub Date:
 January 2020
 arXiv:
 arXiv:2001.10646
 Bibcode:
 2020arXiv200110646B
 Keywords:

 Mathematics  Category Theory;
 Mathematics  Algebraic Geometry;
 Mathematics  Algebraic Topology;
 Mathematics  Representation Theory
 EPrint:
 25 pages. References updated, final version. To appear in Math. Ann