Back to Search Start Over

Neeman's characterization of K(R-Proj) via Bousfield localization

Authors :
Ivo Herzog
Xianhui Fu
Source :
Journal of Pure and Applied Algebra. 222:2288-2291
Publication Year :
2018
Publisher :
Elsevier BV, 2018.

Abstract

Let $R$ be an associative ring with unit and denote by $K({\rm R \mbox{-}Proj})$ the homotopy category of complexes of projective left $R$-modules. Neeman proved the theorem that $K({\rm R \mbox{-}Proj})$ is $\aleph_1$-compactly generated, with the category $K^+ ({\rm R \mbox{-}proj})$ of left bounded complexes of finitely generated projective $R$-modules providing an essentially small class of such generators. Another proof of Neeman's theorem is explained, using recent ideas of Christensen and Holm, and Emmanouil. The strategy of the proof is to show that every complex in $K({\rm R \mbox{-}Proj})$ vanishes in the Bousfield localization $K({\rm R \mbox{-}Flat})/\langle K^+ ({\rm R \mbox{-}proj}) \rangle.$<br />Comment: 5 pages

Details

ISSN :
00224049
Volume :
222
Database :
OpenAIRE
Journal :
Journal of Pure and Applied Algebra
Accession number :
edsair.doi.dedup.....5ae1ce23dab1b3ff74a58ed5876cfa0e