**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 of derived algebraic geometry.

Volume I 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 II 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.

#### Readership

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