The direct limit closure of perfect complexes

Lars Winther Christensen; Henrik Holm

doi:10.1016/j.jpaa.2014.05.004

The direct limit closure of perfect complexes

Lars Winther Christensen, Henrik Holm

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

Every projective module is flat. Conversely, every flat module is a direct limit of finitely generated free modules; this was proved independently by Govorov and Lazard in the 1960s. In this paper we prove an analogous result for complexes of modules, and as applications we reprove some results due to Enochs and García Rozas and to Neeman.

Original language	English
Pages (from-to)	449-463
Number of pages	15
Journal	Journal of Pure and Applied Algebra
Volume	219
Issue number	3
DOIs	https://doi.org/10.1016/j.jpaa.2014.05.004
State	Published - Mar 1 2015

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abstract = "Every projective module is flat. Conversely, every flat module is a direct limit of finitely generated free modules; this was proved independently by Govorov and Lazard in the 1960s. In this paper we prove an analogous result for complexes of modules, and as applications we reprove some results due to Enochs and Garc{\'i}a Rozas and to Neeman.",

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