# A Study in Derived Algebraic Geometry, Part 1: Volume I: Correspondences and Duality

### About this Title

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

Publication: Mathematical Surveys and Monographs

Publication Year:
2017; Volume 221.1

ISBNs: 978-1-4704-3569-1 (print); 978-1-4704-4085-5 (online)

DOI: https://doi.org/10.1090/surv/221.1

MathSciNet review: MR3701352

MSC: Primary 14F05; Secondary 18D05, 18G55

### Table of Contents

**Front/Back Matter**

**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 **