The direct limit closure of perfect complexes

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.

Final version; 16 pp. Some arguments have been simplified or replaced by references to the book of Adámek and Rosický. 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