The Stacks project

69.1 Introduction

In this chapter we put material related to limits of algebraic spaces. A first topic is the characterization of algebraic spaces $F$ locally of finite presentation over the base $S$ as limit preserving functors. We continue with a study of limits of inverse systems over directed sets (Categories, Definition 4.21.1) with affine transition maps. We discuss absolute Noetherian approximation for quasi-compact and quasi-separated algebraic spaces following [CLO]. Another approach is due to David Rydh (see [rydh_approx]) whose results also cover absolute Noetherian approximation for certain algebraic stacks.

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