The direct limit closure of perfect complexes
Rings and Algebras
2013-06-13 v2 Commutative Algebra
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\'ia Rozas and to Neeman.
Cite
@article{arxiv.1301.0731,
title = {The direct limit closure of perfect complexes},
author = {Lars Winther Christensen and Henrik Holm},
journal= {arXiv preprint arXiv:1301.0731},
year = {2013}
}
Comments
Final version; 16 pp. Some arguments have been simplified or replaced by references to the book of Ad\'amek and Rosick\'y. As a consequence, sections 4 and 5 have been merged, and a construction of a certain direct system has been removed. To appear in J. Pure Appl. Algebra