ABSTRACT: Using some methods from stable homotopy theory (e.g. the Brown representability theorem) I shall discuss the following concepts in the context of compactly generated triangulated categories:

• the existence of Auslander-Reiten triangles,
• morphisms determined by objects,
• an Auslander-Reiten formula.

• the stable homotopy category of CW-spectra,
• the derived category of a ring,
• the stable category of modular representations of a finite group.

For further information contact Alex Martsinkovsky <alexmart@neu.edu>