Homology, Homotopy and Applications

Volume 16 (2014)

Number 2

Derived categories of absolutely flat rings

Pages: 45 – 64

DOI: http://dx.doi.org/10.4310/HHA.2014.v16.n2.a3


Greg Stevenson (Fakultät für Mathematik, Universität Bielefeld, Germany)


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.


derived category, absolutely flat ring, localising subcategory, telescope conjecture

2010 Mathematics Subject Classification

16E50, 18E30

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Published 30 November 2014