Let X be a topological space with Noetherian mod p cohomology and let C(X; Fp) be the commutative ring spectrum of Fp-valued cochains on X. We

exhibit conditions under which the category of module spectra over C(X; Fp) is stratied in the sense of Benson, Iyengar, and Krause, providing a classication of all its localizing subcategories. We will explain the setup for these type of results and how can be applied to spaces described as homotopy colimits over finite categories. This is a joint work with T. Barthel, D. Heard and G. Valenzuela.