In this chapter we continue the discussion started in Derived Categories of Schemes, Section 36.1. We will discuss Fourier-Mukai transforms, first studied by Mukai in [Mukai]. We will prove Orlov's theorem on derived equivalences ([Orlov-K3]). We also discuss the countability of derived equivalence classes proved by Anel and Toën in [AT].
A good introduction to this material is the book [Huybrechts] by Daniel Huybrechts. Some other papers which helped popularize this topic are
the paper by Bondal and Kapranov, see [Bondal-Kapranov]
the paper by Bondal and Orlov, see [Bondal-Orlov]
the paper by Bondal and Van den Bergh, see [BvdB]
the paper by Orlov, see [Orlov-AV]
the paper by Orlov, see [Orlov-motives]
the paper by Rouquier, see [Rouquier-dimensions]
there are many more we could mention here.
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