Strong generation of the bounded derived category of coherent sheaves

An object G of a triangulated category is a strong generator if there is an integer N, so that every object is obtainable from direct sums of shifts of G using no more than N triangles (and possibly taking direct summands). The smallest N which works is called the dimension of the triangulated category, and there has been much literature on this in recent years. We will review the results. The new theorem we wish to report is that the bounded derived category of coherent sheaves on a scheme X has a strong generator, provided X is essentially of finite type over an excellent scheme of dimension no more than two.