## 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 [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 papers by Beilinson, see [Beilinson] and [Beilinson-derived]

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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