Rational G-spectra over blocks 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. [Version 2 fills several gaps. (a) The selection of conjugacy class representatives (b) smallness of generators (c) compatibility of Morita equivalences with diagram (d) definition of complete model. Exposition and notational consistency improved.]