Book project: A Study in Derived Algebraic Geometry (D. Gaitsgory and N. Rozenblyum)

The published version

• Volume 1
• Volume 2

Chapter-by-chapter original version

Introductions

• Preface
• Introduction to Volume-I
• Introduction to Volume-II

Part I: Preliminaries

• Introduction to Part I
• Chapter I.1: Some higher algebra
• Chapter I.2: Basics of derived algebraic geometry
• Chapter I.3: Quasi-coherent sheaves on prestacks

Part II: Ind-coherent sheaves

• Introduction to Part II
• Chapter II.1: Ind-coherent sheaves on schemes
• Chapter II.2: Ind-coherent sheaves as a functor out of the category of correspondences
• Chapter II.3: Interaction of QCoh and IndCoh

Part III: Inf-schemes

• Introduction to Part III
• Chapter III.1: Deformation theory
• Chapter III.2: Ind-schemes and inf-schemes
• Chapter III.3: Ind-coherent sheaves on ind-inf-schemes
• Chapter III.4: An application: crystals

Part IV: Formal Geometry

• Introduction to Part IV
• Chapter IV.1: Formal moduli
• Chapter IV.2: Lie algebras and co-commutative co-algebras
• Chapter IV.3: Formal groups and Lie algebras
• Chapter IV.4: Lie algebroids
• Chapter IV.5: Infinitesimal differential geometry

Categories of correspondences

• Introduction to Part V
• Chapter V.1: The (oo,2)-category of correspondences
• Chapter V.2: Extension theorems for the category of correspondences
• Chapter V.3: The (symmetric) monoidal structure on the category of correspondences

Appendix: (oo,2)-categories

• Introduction to Part A
• Chapter A.1: Basics of 2-categories
• Chapter A.2: Straightening and Yoneda for (oo,2)-categories
• Chapter A.3: Adjunctions in (oo,2)-categories

References

• Notations
• Glossary
• References