A Study in Derived Algebraic Geometry : Volume I: Correspondences and Duality Hardback
by Dennis Gaitsgory, Nick Rozenblyum
Part of the Mathematical Surveys and Monographs series
Hardback
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 volume develops the theory of ind-coherent sheaves in the context of derived algebraic geometry.
Ind-coherent sheaves 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. This volume consists of three parts and an appendix.
The first part is a survey of homotopical algebra in the setting of $\infty$-categories and the basics of derived algebraic geometry.
The second part builds the theory of ind-coherent sheaves as a functor out of the category of correspondences and studies the relationship between ind-coherent and quasi-coherent sheaves.
The third part sets up the general machinery of the $\mathrm{(}\infty, 2\mathrm{)}$-category of correspondences needed for the second part.
The category of correspondences, via the theory developed in the third part, provides a general framework for Grothendieck's six-functor formalism.
The appendix provides the necessary background on $\mathrm{(}\infty, 2\mathrm{)}$-categories needed for the third part.
Information
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Item not Available
- Format:Hardback
- Pages:553 pages
- Publisher:American Mathematical Society
- Publication Date:30/07/2017
- Category:
- ISBN:9781470435691
Other Formats
- Paperback / softback from £113.00
Information
-
Item not Available
- Format:Hardback
- Pages:553 pages
- Publisher:American Mathematical Society
- Publication Date:30/07/2017
- Category:
- ISBN:9781470435691
