## 74.1 Introduction

In the chapter on topologies on algebraic spaces (see Topologies on Spaces, Section 73.1) we introduced étale, fppf, smooth, syntomic and fpqc coverings of algebraic spaces. In this chapter we discuss what kind of structures over algebraic spaces can be descended through such coverings. See for example [Gr-I], [Gr-II], [Gr-III], [Gr-IV], [Gr-V], and [Gr-VI].

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