For a derived category of a Noetherian ring (or perhaps more generally), can we talk about a Periodicity Theorem? We have Thick Subcategory Theorems and Nilpotence Theorems (HPS 91) for D(R), and in some more general cases, but I haven't seen, in my limited review of the literature, a theorem describing how such data might "stratify" the endomorphisms of the unit object (in this case I guess R). Or, in a similar vein, finding specific maps whose cofiber lies in perhaps the "next higher" level. Perhaps this is connected to the fact that for a ring, unlike in the case of finite p-local spectra, there isn't really a linear ordering of primes, necessarily. Anyone know of any work on this idea? Or perhaps know a straightforward answer?

Thanks!