A STUDY IN DERIVED ALGEBRAIC GEOMETRY. VOLUMES I AND II

A STUDY IN DERIVED ALGEBRAIC GEOMETRY. VOLUMES I AND II

Editorial:
AMS (AMERICAN MATHEMATICAL SOCIETY)
Año de edición:
Materia
Matematicas
ISBN:
978-1-4704-3568-4
Páginas:
1016
N. de edición:
1
Idioma:
Inglés
Disponibilidad:
Disponible en 2-3 semanas

Descuento:

-5%

Antes:

242,32 €

Despues:

230,20 €

• 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.

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.