Green equivalences in equivariant mathematics
Category Theory
2022-02-24 v2 Algebraic Geometry
Algebraic Topology
Representation Theory
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.
Keywords
Cite
@article{arxiv.2001.10646,
title = {Green equivalences in equivariant mathematics},
author = {Paul Balmer and Ivo Dell'Ambrogio},
journal= {arXiv preprint arXiv:2001.10646},
year = {2022}
}
Comments
25 pages. References updated, final version. To appear in Math. Ann