APPLICATIONS OF COTORSION PAIRS

Abstract

For an artin algebra Λ, cotorsion pairs are studied for the category Mod Λ of finitely presented Λ-modules and for the category Mod Λ of all Λ-modules. It is shown that every cotorsion pair for Mod Λ induces a cotorsion pair for Mod Λ. 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.