In 1996, Jens Franke proved the equivalence of certain triangulated categories possessing an Adams spectral sequence. One particular application of this theorem is that the K(p)-local stable homotopy category at an odd prime can be described as the derived category of an abelian category. We explain this proof from a topologist's point of view.
Homology, Homotopy and Applications, Vol. 10 (2008), No. 1, pp.389-412.