A Study in Derived Algebraic Geometry : Volumes I and II Hardback
Part of the Mathematical Surveys and Monographs series
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.
- Format: Hardback
- Pages: 1016 pages
- Publisher: American Mathematical Society
- Publication Date: 30/07/2017
- Category: Algebraic geometry
- ISBN: 9781470435684