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 : 13,5 Mb
If you're still pondering over how to secure a PDF or EPUB version of the book A Study in Derived Algebraic Geometry by Dennis Gaitsgory, don't worry! All you have to do is click the 'Get Book' buttons below to kick off your Download or Read Online journey. Just a friendly reminder: we don't upload or host the files ourselves.