English

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

Representation Theory 2017-04-04 v1 Rings and Algebras

Abstract

Let RR be an associative ring with unit and denote by K(R\mboxProj)K({\rm R \mbox{-}Proj}) the homotopy category of complexes of projective left RR-modules. Neeman proved the theorem that K(R\mboxProj)K({\rm R \mbox{-}Proj}) is 1\aleph_1-compactly generated, with the category K+(R\mboxproj)K^+ ({\rm R \mbox{-}proj}) of left bounded complexes of finitely generated projective RR-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(R\mboxProj)K({\rm R \mbox{-}Proj}) vanishes in the Bousfield localization K(R\mboxFlat)/K+(R\mboxproj).K({\rm R \mbox{-}Flat})/\langle K^+ ({\rm R \mbox{-}proj}) \rangle.

Keywords

Cite

@article{arxiv.1704.00233,
  title  = {Neeman's characterization of K(R-Proj) via Bousfield localization},
  author = {Xianhui Fu and Ivo Herzog},
  journal= {arXiv preprint arXiv:1704.00233},
  year   = {2017}
}

Comments

5 pages