A Study in Derived Algebraic Geometry is popular PDF and ePub book, written by Dennis Gaitsgory in 2019-12-31, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, A Study in Derived Algebraic Geometry can be Read Online from any device for your convenience.
A Study in Derived Algebraic Geometry Book PDF Summary
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 $mathrm{(}infty, 2mathrm{)}$-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 $mathrm{(}infty, 2mathrm{)}$-categories needed for the third part.
Detail Book of A Study in Derived Algebraic Geometry PDF
- Author : Dennis Gaitsgory
- Release : 31 December 2019
- Publisher : American Mathematical Society
- ISBN : 9781470452841
- Genre : Mathematics
- Total Page : 533 pages
- Language : English
- PDF File Size : 15,5 Mb
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