Tuesday, January 19, 14:00, 7.527

Sebastian Nitsche, The stable module category inside the homotopy category

Abstract:
We consider a functor from the stable module category to the homotopy category constructed by Kato. This functor induces a correspondence between distinguished triangles in the homotopy category and perfect exact sequences in the module category.
In this talk, we discuss stable equivalences that preserve perfect exact sequences and apply this to the stable category of Gorenstein-projective modules. Moreover, this provides conditions under which a stable equivalence induced by an exact functor is a stable equivalence of Morita type. We also give a description of a triangulated hull of the stable module category inside the homotopy category.