On the structure of modules over wild hereditary algebras

Let H be a connected finite dimensional wild hereditary path-algebra over an arbitrary field K and tau(H) the Auslander-Reiten translation on H-mod, the category of finite dimensional H-modules. Let X be a finite dimensional H-module. We prove unexpected new results on the structure of the shifted modules tau(H)(m) X, for \m\ >> 0, their minimal projective and injective resolutions, and the Auslander-Reiten components of the one-point extensions and coextensions of H by the modules tau(H)(m) X.