Derived categories of absolutely flat rings

Abstract

Let S be a commutative ring with topologically noetherian spectrum and let R be the absolutely flat approximation of S. We prove that subsets of the spectrum of R parametrise the localising subcategories of D(R). Moreover, we prove the telescope conjecture holds for D(R). We also consider unbounded derived categories of absolutely flat rings which are not semi-artinian and exhibit an example of a cohomological Bousfield class that is not a Bousfield class.