Some remarks on projective Mackey functors
This paper discusses Mackey functors on a finite group \(G\). Among the results are the following: a Mackey functor has projective dimension 0, 1 or \(\infty\); the Grothendieck \(G\)-theory of Mackey functors is computable in terms of the \(G\)-theories of Weyl groups; the same applies to \(K\)- theory for Mackey functors whose values are modules over a ring in which the order of \(G\) is invertible. The author also computes the projective class groups of Mackey functors for groups of prime order and gives applications to equivariant stable homotopy theory. In particular, there is no stable \(G\)-Moore spectrum for the integers if \(G\) is a non-trivial.
scientific article; zbMATH DE number 64209
scientific article