In this talk I will present joint work with K. Arnesen, D. Pauksztello and M. Prest. We classify the indecomposable pure-injective complexes in the homotopy category of projective modules K(ProjΛ) over a derived-discrete algebra Λ. The set of indecomposable pure-injective complexes are the points of a topological space known as the Ziegler spectrum. We give a complete description of the Ziegler topology and, making use of the interactions between this space and categories of functors, we prove that every indecomposable object in K(ProjΛ) is pure-injective.
This video was produced by Syracuse University Department of Mathematics as part of ICRA 2016.
