  For G an arbitrary profinite group, we construct an algebraic model for
rational G-spectra in terms of G-equivariant sheaves over the space of
subgroups of G. This generalises the known case of finite groups to a much
wider class of topological groups, and improves upon earlier work of the first
author on the case where G is the p-adic integers.
  As the purpose of an algebraic model is to allow one to use homological
algebra to study questions of homotopy theory, we prove that the homological
dimension (injective dimension) of the algebraic model is determined by the
Cantor--Bendixson rank of the space of closed subgroups of the profinite group
G. This also provides a calculation of the homological dimension of the
category of rational Mackey functors.
