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We characterize the separated schemes for which the derived category ofperfect complexes is strongly generated, proving a conjecture of Bondal and Vanden Bergh. And we also prove the strong generation of the bounded derivedcategory of coherent sheaves under mild conditions.  In the proof we introduce techniques that have shown themselves to havepowerful consequences in other contexts. In this final, pre-publication versionof the manuscript there is a (very brief) survey of subsequent, followuparticles.

Strong generators in $D^{perf}(X)$ and $D^b_{coh}(X)$