Cotorsion theories, model category structures, and representation theory
by Mark Hovey
mhovey@wesleyan.edu
AMS Classification: 20C05,20J05,18E30,18G35, 55U35
We make a general study of Quillen model structures on abelian
categories. Given a proper class P of short exact sequences on an
abelian cateory A, we define what it means for a model structure to be
compatible with P. We then give a complete characterization of model
structures compatible with P. This characterization is in terms of
cotorsion theories, which were introduced by Salce and have been much
studied recently by Enochs and coauthors. We apply the general method
to construct a stable category of $K[G]$-modules where $K$ is a
principal ideal domain and $G$ is a finite group. This is a compactly
generated triangulated category that generalizes the well-known stable
category of $k[G]$-modules, where $k$ is a field.