arXiv:1108.6309 On the Algebraic Classification of Module Spectra from arXiv Front: math.KT by Irakli Patchkoria Using methods developed by Franke, we obtain algebraic classification results for modules over certain symmetric ring spectra (-algebras). In particular, for any symmetric ring spectrum whose graded homotopy ring has graded global homological dimension 2 and is concentrated in degrees divisible by some natural number , we prove that the homotopy category of -modules is equivalent to the derived category of the homotopy ring . This improves the Bousfield-Wolbert algebraic classification of isomorphism classes of objects of the homotopy category of -modules. The main examples of ring spectra to which our result applies are the -local real connective -theory spectrum , the Johnson-Wilson spectrum E(2), and the truncated Brown-Peterson spectrum , for an odd prime .
nLab page on Module spectra