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Overview"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 two-volume monograph develops generalization of various topics in algebraic geometry in the context derived algebraic geometry. Volume 1 presents the theory of ind-coherent sheaves, which 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. Volume 2 develops deformation theory, Lie theory and the theory of algebroids in the context of derived algebraic geometry. To that end, it introduces the notion of inf-scheme, which is an infinitesimal deformation of a scheme and studies ind-coherent sheaves on inf-schemes. As an application of the general theory, the six-functor formalism for D-modules in derived geometry is obtained." Full Product DetailsAuthor: Dennis Gaitsgory , Nick RozenblyumPublisher: American Mathematical Society Imprint: American Mathematical Society ISBN: 9781470435684ISBN 10: 1470435683 Pages: 1016 Publication Date: 30 August 2017 Audience: College/higher education , Postgraduate, Research & Scholarly Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsContents for Volume I: Preliminaries: Introduction Some higher algebra Basics of derived algebraic geometry Quasi-coherent sheaves on prestacks Ind-coherent sheaves: Introduction Ind-coherent sheaves on schemes Ind-coherent sheaves as a functor out of the category of correspondences Interaction of Qcoh and IndCoh Categories of correspondences: Introduction The $(\infty,2)$-category of correspondences Extension theorems for the category of correspondences The (symmetric) monoidal structure on the category of correspondences $(\infty,2)$-categories: Introduction Basics of 2-categories Straightening and Yoneda for $(\infty,2)$-categories Adjunctions in $(\infty,2)$-categories Bibliography Index of notations Index Contents for Volume II: Inf-schemes: Introduction Deformation theory Ind-schemes and inf-schemes Ind-coherent sheaves on ind-inf-schemes An application: Crystals Formal geometry: Introduction Formal moduli Lie algebras and co-commutative co-algebras Formal groups and Lie algebras Lie algebroids Infinitesimal differential geometry Bibliography Index of notations Index.ReviewsAuthor InformationDennis Gaitsgory, Harvard University, Cambridge, MA. Nick Rozenblyum, University of Chicago, IL. Tab Content 6Author Website:Countries AvailableAll regions |
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