Homology, Homotopy and Applications

Derived categories of absolutely flat rings

Greg Stevenson

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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

Permanent link to this document
https://projecteuclid.org/euclid.hha/1408712334

Mathematical Reviews number (MathSciNet)
MR3234500

Zentralblatt MATH identifier
1304.83022

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

Keywords
Derived category absolutely flat ring localising subcategory telescope conjecture

Citation

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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