Overview

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.

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9781470453060

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Reviews

The books are carefully written...and they are not as difficult to read as one might expect from the content. This is mainly due to the many introductions scattered throughout the books, which explain the main ideas of each volume, part or chapter. -Adrian Langer, Mathematical Reviews

Author Information

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

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