A Study in Derived Algebraic Geometry: Correspondences and Duality (Mathematical Surveys and Monographs) by Dennis Gaitsgory (PDF)

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 $mathrm{(}infty, 2mathrm{)}$-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.

User’s Reviews

Editorial Reviews: About the Author Dennis Gaitsgory, Harvard University, Cambridge, MA.Nick Rozenblyum, University of Chicago, IL.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐

⭐

Keywords

Free Download A Study in Derived Algebraic Geometry: Correspondences and Duality (Mathematical Surveys and Monographs) in PDF format
A Study in Derived Algebraic Geometry: Correspondences and Duality (Mathematical Surveys and Monographs) PDF Free Download
Download A Study in Derived Algebraic Geometry: Correspondences and Duality (Mathematical Surveys and Monographs) 2017 PDF Free
A Study in Derived Algebraic Geometry: Correspondences and Duality (Mathematical Surveys and Monographs) 2017 PDF Free Download
Download A Study in Derived Algebraic Geometry: Correspondences and Duality (Mathematical Surveys and Monographs) PDF
Free Download Ebook A Study in Derived Algebraic Geometry: Correspondences and Duality (Mathematical Surveys and Monographs)