A Study in Derived Algebraic Geometry
American Mathematical Society (Verlag)
978-1-4704-3568-4 (ISBN)
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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.
Dennis Gaitsgory, Harvard University, Cambridge, MA. Nick Rozenblyum, University of Chicago, IL.
Contents 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.
| Erscheinungsdatum | 10.08.2017 |
|---|---|
| Reihe/Serie | Mathematical Surveys and Monographs |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-4704-3568-3 / 1470435683 |
| ISBN-13 | 978-1-4704-3568-4 / 9781470435684 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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