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A study in derived algebraic geometry. Volume I, Correspondences and duality

Author: D Gaitsgory; Nick Rozenblyum
Publisher: Providence : American Mathematical Society, 2017.
Series: Mathematical surveys and monographs.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Gaitsgory, Dennis.
Study in Derived Algebraic Geometry.
Providence : American Mathematical Society, 2017
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: D Gaitsgory; Nick Rozenblyum
ISBN: 9781470440855 1470440857
OCLC Number: 1000452377
Description: 1 online resource (577 pages).
Contents: Preliminaries: IntroductionSome higher algebraBasics of derived algebraic geometryQuasi-coherent sheaves on prestacksInd-coherent sheaves: IntroductionInd-coherent sheaves on schemesInd-coherent 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 2-categoriesStraightening and Yoneda for $(\infty,2)$-categoriesAdjunctions in $(\infty,2)$-categoriesBibliographyIndex of notationsIndex.
Series Title: Mathematical surveys and monographs.
Responsibility: Dennis Gaitsgory, Nick Rozenblyum.

Abstract:

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  Read more...

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