Finiteness conditions and cotorsion pairs

We study the interplay between the notions of n-coherent rings and finitely n-presented modules, and also study the relative homological algebra associated to them. We show that the n-coherency of a ring is equivalent to the thickness of the class of finitely n-presented modules. The relative homological algebra part comes from the study of orthogonal complements to this class of modules with respect to the Ext and Tor functors. We also construct cotorsion pairs from these orthogonal complements, allowing us to provide further characterizations of n-coherent rings.