Given a cotorsion pair (A, B) in an abelian category C with enough A objects and enough B objects, we define two cotorsion pairs in the category Ch(C) of unbounded chain complexes. We see that these two cotorsion pairs are related in a nice way when (A, B) is hereditary. We then show that both of these induced cotorsion pairs are complete when (A, B) is the "flat" co-torsion pair of R-modules. This proves the flat cover conjecture for (possibly unbounded) chain complexes and also gives us a new "flat" model category structure on Ch(R). In the last section we use the theory of model categories to show that we can define Ext n R (M, N) using a flat resolution of M and a cotorsion coresolution of N .
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