## 57.1 Introduction

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 by Daniel Huybrechts. Some other papers which helped popularize this topic are

1. the paper by Bondal and Kapranov, see

2. the paper by Bondal and Orlov, see

3. the paper by Bondal and Van den Bergh, see [BvdB]

4. the papers by Beilinson, see and

5. the paper by Orlov, see [Orlov-AV]

6. the paper by Orlov, see

7. the paper by Rouquier, see

8. there are many more we could mention here.

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