5 Introduction

Chapters in this book

1. Frontmatter I
2. Preface to the second edition VII
3. Introduction IX
4. Contents XV
5. Part I: Prerequisites
6. 1 Schemes 3
7. 2 Simplicial sets 12
8. 3 ∞-categories 16
9. 4 Model categories 27
10. Part II: Derived algebraic geometry
11. 5 Introduction 51
12. 6 Stacks on simplicial sites 53
13. 7 Stacks on model sites 58
14. 8 Stacks on Segal sites 64
15. 9 Application: étale derived stacks 69
16. Part III: Spectral algebraic geometry
17. 10 Introduction 75
18. 11 ∞-operads 77
19. 12 Spectra 81
20. 13 E∞-ring spectra 83
21. 14 Spectral Deligne–Mumford stacks 85
22. 15 Spectral Artin representability 88
23. 16 Representation theory of formal moduli problems 97
24. 17 Relations between quasi-coherent sheaves 100
25. Part IV: Applications
26. 18 A dual representation in spectral algebraic geometry 107
27. 19 A Connection SAG-DAG 114
28. 20 Motifs in DAG 117
29. 21 Introduction to a category of derived motivic spectra 136
30. 22 Goodwillie calculus and geometric stacks 160
31. 23 Spectral “schematization” of homotopy types 185
32. 24 Higher Galois for Segal topos 201
33. 25 Infinity-topoi and natural phenomena: generation 212
34. 26 Segal topoi and the universality of physical laws 224
35. 27 Internal Bousfield localizations 237
36. 28 Supersymmetric derived stacks 267
37. 29 Taking stock – Physical Mathematics 320
38. Bibliography 349
39. Index 353
40. Notations 359