Title: Point-tree topology and Hochster duality in derived categories Abstract: For R a commutative ring, we give an explicit realisation of both the Zariski frame of R and its Hochster dual frame, as lattices in the poset of localising subcategories of the unbounded derived category D(R). This yields new conceptual proofs of the classical theorems of Hopkins-Neeman and Thomason. This is joint work with Wolfgang Pitsch, available at [arXiv:1305.1503].