Study in Derived Algebraic Geometry

Volumes I and II

Inbunden, Engelska, 2017

Av Dennis Gaitsgory, Nick Rozenblyum

3 949 kr

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Häftad

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Häftad

1 959 kr

Skickas inom 10-15 vardagar

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.

Produktinformation

Utgivningsdatum2017-07-30
Mått178 x 254 x undefined mm
FormatInbunden
SpråkEngelska
SerieMathematical Surveys and Monographs
FörlagAmerican Mathematical Society
ISBN9781470435684

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Matematik inom Naturvetenskap och teknik

Contents for Volume I: 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 notationsIndexContents for Volume II: Inf-schemes: IntroductionDeformation theoryInd-schemes and inf-schemesInd-coherent sheaves on ind-inf-schemesAn application: CrystalsFormal geometry: IntroductionFormal moduliLie algebras and co-commutative co-algebrasFormal groups and Lie algebrasLie algebroidsInfinitesimal differential geometryBibliographyIndex of notationsIndex.