A Study in Derived Algebraic Geometry

Dennis Gaitsgory, Harvard University, Cambridge, MA. Nick Rozenblyum, University of Chicago, IL.

Contents for Volume I:
Preliminaries: Introduction
Some higher algebra
Basics of derived algebraic geometry
Quasi-coherent sheaves on prestacks
Ind-coherent sheaves: Introduction
Ind-coherent sheaves on schemes
Ind-coherent sheaves as a functor out of the category of correspondences
Interaction of Qcoh and IndCoh
Categories of correspondences: Introduction
The $(/infty,2)$-category of correspondences
Extension theorems for the category of correspondences
The (symmetric) monoidal structure on the category of correspondences
$(/infty,2)$-categories: Introduction
Basics of 2-categories
Straightening and Yoneda for $(/infty,2)$-categories
Adjunctions in $(/infty,2)$-categories
Bibliography
Index of notations
Index
Contents for Volume II:
Inf-schemes: Introduction
Deformation theory
Ind-schemes and inf-schemes
Ind-coherent sheaves on ind-inf-schemes
An application: Crystals
Formal geometry: Introduction
Formal moduli
Lie algebras and co-commutative co-algebras
Formal groups and Lie algebras
Lie algebroids
Infinitesimal differential geometry
Bibliography
Index of notations
Index.