**Mathematical Surveys and Monographs**

Volume: 221;
2017;
Hardcover
**Print ISBN: 978-1-4704-3568-4
Product Code: SURV/221**

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# A Study in Derived Algebraic Geometry: Volumes I and II

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*Dennis Gaitsgory; Nick Rozenblyum*

Derived algebraic geometry is a far-reaching generalization of
algebraic geometry. It has found numerous applications in various
parts of mathematics, most prominently in representation theory. This
two-volume monograph develops generalization of various topics in
algebraic geometry in the context derived algebraic geometry.

Volume 1 presents the theory of ind-coherent sheaves, which are a
“renormalization” of quasi-coherent sheaves and provide a natural
setting for Grothendieck-Serre duality as well as geometric
incarnations of numerous categories of interest in representation
theory.

Volume 2 develops deformation theory, Lie theory and the theory of
algebroids in the context of derived algebraic geometry. To that end,
it introduces the notion of inf-scheme, which is an infinitesimal
deformation of a scheme and studies ind-coherent sheaves on
inf-schemes. As an application of the general theory, the six-functor
formalism for D-modules in derived geometry is obtained.

#### Table of Contents

# Table of Contents

## A Study in Derived Algebraic Geometry: Volumes I and II

#### Readership

Graduate students and researchers interested in new trends in algebraic geometry and representation theory.