A Study in Derived Algebraic Geometry : Volumes I and II Paperback / softback
by Dennis Gaitsgory, Nick Rozenblyum
Part of the Mathematical Surveys and Monographs series
Paperback / softback
Description
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.
Information
-
Available to Order - This title is available to order, with delivery expected within 2 weeks
- Format:Paperback / softback
- Pages:969 pages
- Publisher:American Mathematical Society
- Publication Date:30/12/2017
- Category:
- ISBN:9781470453060
Information
-
Available to Order - This title is available to order, with delivery expected within 2 weeks
- Format:Paperback / softback
- Pages:969 pages
- Publisher:American Mathematical Society
- Publication Date:30/12/2017
- Category:
- ISBN:9781470453060
