Applications of cotorsion pairs

Krause H, Solberg Ø. Applications of cotorsion pairs. Journal of the London Mathematical Society. 2. Series. 2003;68(3):631-650.For an artin algebra Lambda, cotorsion pairs are studied for the category mod A of finitely presented Lambda-modules and for the category Mod Lambda of all Lambda-modules. It is shown that every cotorsion pair for mod Lambda induces a cotorsion pair for Mod Lambda. This has some interesting applications, even for the category of finitely presented modules. Another theme of the paper is the interplay between cotorsion and torsion pairs. This leads to a conjecture which is an analogue of the telescope conjecture in stable homotopy theory