Etale Equivalence Relations

Abstract

In the first section of this chapter, we will first recall the definition and the first properties of étale equivalence relations.We restrict our presentation to the notions we will need in the next chapters; for more details see, for example, [74, 78, 80]. In the second section, we recall the definitions of isomorphism and orbit equivalence of étale equivalence relations. In the second section, we define AF-equivalence relations, a rich but also tractable class of étale equivalence relations that we will classify up to isomorphism and up to orbit equivalence, respectively, in Section 20.5 and Chapter 22.