## Homology, Homotopy and Applications

### Derived categories of absolutely flat rings

Greg Stevenson

#### 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 $\mathsf{D}(R)$. Moreover, we prove the telescope conjecture holds for $\mathsf{D}(R)$. We also consider unbounded derived categories of absolutely flat rings that are not semi-artinian and exhibit a localising subcategory that is not a Bousfield class and a cohomological Bousfield class that is not a Bousfield class.

#### Article information

Source
Homology Homotopy Appl. Volume 16, Number 2 (2014), 45-64.

Dates
First available in Project Euclid: 22 August 2014