Rational G-spectra over blocks with finite Weyl groups

TL;DR

This paper establishes an equivalence between certain categories of G-spectra with specified isotropy and equivariant sheaves, providing an algebraic model with bounded injective dimension for groups with finite Weyl groups.

Contribution

It introduces an algebraic model for G-spectra over blocks with finite Weyl groups, connecting geometric isotropy with equivariant sheaves.

Findings

Category of G-spectra with geometric isotropy in X is equivalent to equivariant sheaves over X

Provides an algebraic model with injective dimension at most the rank of G

Applicable to groups with finite Weyl groups

Abstract

We show that for any clopen collection X of subgroups of G with finite Weyl groups, the category of G-spectra with geometric isotropy in X is equivalent to the category of equivariant sheaves over X. This gives an algebraic model of injective dimension at most the rank of G.