A Study in Derived Algebraic Geometry: Volume I: Correspondences and Duality (Mathematical Surveys and Monographs) - Softcover

Dennis Gaitsgory; Nick Rozenblyum

Softcover

ISBN 10: 1470452847 ISBN 13: 9781470452841

Publisher: American Mathematical Society, 2019

Synopsis

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 ∞-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 (∞,2)-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 (∞,2)-categories needed for the third part.

About this title

About the Author

Dennis Gaitsgory: Harvard University, Cambridge, MA, Nick Rozenblyum: University of Chicago, Chicago, IL

Edition details

• Publisher: American Mathematical Society
• Publication date: 2019
• Language: English
• ISBN 10: 1470452847
• ISBN 13: 9781470452841
• Binding: Paperback
• Number of pages: 533