Contents

1 Introduction
 1.1 What's HAG ?
 1.2 What's DAG ?
2 The model category of D-stacks
 2.1 D-Pre-stacks
 2.2 D-Stacks
 2.3 Operations on D-stacks
3 First examples of D-stacks
 3.1 Representables
 3.2 Stacks vs. D-stacks
 3.3 dg-Schemes
 3.4 The D-stack of G-torsors
4 The geometry of D-stacks
 4.1 Geometricity
 4.2 Modules, linear D-stacks and K-theory
 4.3 Tangent D-stacks
 4.4 Smoothness
5 Further examples
 5.1 Local systems on a topological space
 5.2 Vector bundles on a projective variety
 5.3 Algebras and A¥-categorical structures
6 Final comments on deriving moduli functors