Silting objects, simple-minded collections, t-structures and co-t-structures for finite-dimensional algebras

Bijective correspondences are established between (1) silting objects, (2) simple-minded collections, (3) bounded t -structures with length heart and (4) bounded co- t -structures. These correspondences are shown to commute with mutations and partial orders. The results are valid for finite-dimensional algebras. A concrete example is given to illustrate how these correspondences help to compute the space of Bridgeland's stability conditions.