Homology, Homotopy and Applications

Derived categories of absolutely flat rings

Greg Stevenson

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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

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

First available in Project Euclid: 22 August 2014

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 18E30: Derived categories, triangulated categories 16E50: von Neumann regular rings and generalizations

Derived category absolutely flat ring localising subcategory telescope conjecture


Stevenson, Greg. Derived categories of absolutely flat rings. Homology Homotopy Appl. 16 (2014), no. 2, 45--64. https://projecteuclid.org/euclid.hha/1408712334.

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