A Study in Derived Algebraic Geometry (Innbundet)

Volumes I and II

Serie: Mathematical Surveys and Monographs 



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Forfatter: og
Innbinding: Innbundet
Utgivelsesår: 2017
Antall sider: 1016
Forlag: American Mathematical Society
Språk: Engelsk
Serie: Mathematical Surveys and Monographs
ISBN/EAN: 9781470435684
Omtale A Study in Derived Algebraic Geometry
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.

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