A study in derived algebraic geometry
 Responsibility
 Dennis Gaitsgory, Nick Rozenblyum.
 Publication
 Providence, Rhode Island : American Mathematical Society, [2017]
 Physical description
 2 volumes ; 27 cm.
 Series
 Mathematical surveys and monographs ; no. 221.
Access
Available online
Science Library (Li and Ma)
Stacks
Library has: v.1v.2 <v.221 in series>
Call number  Status 

QA3 .A4 V.221:PT.1  Unknown 
QA3 .A4 V.221:PT.2  Unknown 
More options
Creators/Contributors
 Author/Creator
 Gaitsgory, D. (Dennis) author.
 Contributor
 Rozenblyum, Nick, 1984 author.
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 Preliminaries: IntroductionSome higher algebraBasics of derived algebraic geometryQuasicoherent sheaves on prestacksIndcoherent sheaves: IntroductionIndcoherent sheaves on schemesIndcoherent sheaves as a functor out of the category of correspondencesInteraction of Qcoh and IndCohCategories of correspondences: IntroductionThe $(\infty, 2)$category of correspondencesExtension theorems for the category of correspondencesThe (symmetric) monoidal structure on the category of correspondences$(\infty, 2)$categories: IntroductionBasics of 2categoriesStraightening and Yoneda for $(\infty, 2)$categoriesAdjunctions in $(\infty, 2)$categoriesBibliographyIndex of notationsIndex.
 (source: Nielsen Book Data)9781470435691 20170821
 Publisher's Summary
 Derived algebraic geometry is a farreaching 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 indcoherent sheaves in the context of derived algebraic geometry. Indcoherent sheaves are a ``renormalization'' of quasicoherent sheaves and provide a natural setting for GrothendieckSerre 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 indcoherent sheaves as a functor out of the category of correspondences and studies the relationship between indcoherent and quasicoherent sheaves. The third part sets up the general machinery of the $\mathrm{(}\infty, 2\mathrm{)}$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 sixfunctor formalism. The appendix provides the necessary background on $\mathrm{(}\infty, 2\mathrm{)}$categories needed for the third part.
(source: Nielsen Book Data)9781470435691 20170821
Subjects
 Subject
 Geometry, Algebraic.
 Duality theory (Mathematics)
 Lie algebras.
 Geometry.
 Duality theory (Mathematics)
 Geometry.
 Geometry, Algebraic.
 Lie algebras.
 Algebraic geometry > Research exposition (monographs, survey articles)
 Algebraic geometry > Foundations > Generalizations (algebraic spaces, stacks)
 Algebraic geometry > (Colo.)homology theory > Sheaves, derived categories of sheaves and related constructions.
 Algebraic geometry > Families, fibrations > Formal methods; deformations.
 Algebraic geometry > (Colo.)homology theory > Differentials and other special sheaves; Dmodules; BernsteinSato ideals and polynomials.
 Category theory; homological algebra > Homological algebra > Homotopical algebra.
 Category theory; homological algebra > Categories with structure > Double categories, $2$categories, bicategories and generalizations.
Bibliographic information
 Beginning date
 2017
 Ending date
 2017
 Series
 Mathematical surveys and monographs ; volume 221
 ISBN
 9781470435691 hardcover alkaline paper volume 1
 1470435691 hardcover alkaline paper volume 1
 9781470435707 hardcover alkaline paper volume 2