A Study in Derived Algebraic Geometry: Volumes I and II - Mathematical Surveys and Monographs (Hardback)
  • A Study in Derived Algebraic Geometry: Volumes I and II - Mathematical Surveys and Monographs (Hardback)
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A Study in Derived Algebraic Geometry: Volumes I and II - Mathematical Surveys and Monographs (Hardback)

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£210.00
Hardback 1016 Pages / Published: 30/08/2017
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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.

Publisher: American Mathematical Society
ISBN: 9781470435684
Number of pages: 1016
Dimensions: 254 x 178 mm

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