Rational G-spectra for profinite G

The algebraic model we consider is chain complexes of Weyl-G-sheaves of Q-modules over the space SG. The key step in proving that this is an algebraic model for G-spectra is in proving that the category of rational G-Mackey functors is equivalent to Weyl-G-sheaves.

In addition to the fact that this sheaf description utilises the topology of G and the closed subgroups of G in a more explicit way than Mackey functors do, we can also calculate the injective dimension. In the final part of the thesis we will see that the injective dimension of the category of Weyl-G-sheaves can be calculated in terms of the Cantor- Bendixson rank of SG, hence giving the injective dimension of the category of Mackey functors via the earlier equivalence.