A01=Dennis Gaitsgory
A01=Nick Rozenblyum
algebra
algebraic geometry
Author_Dennis Gaitsgory
Author_Nick Rozenblyum
Category=PBMW
eq_isMigrated=0
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
extension theorems
formal groups
formal moduli
lie algebras
math
mathematics
maths
monoidal structure
Product details
- ISBN 9781470453060
- Publication Date: 30 Dec 2017
- Publisher: American Mathematical Society
- Publication City/Country: US
- Product Form: Paperback
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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 of derived algebraic geometry.
Volume I 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 II 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.
Volume I 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 II 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, Chicago, IL.
Nick Rozenblyum, University of Chicago, Chicago, IL.
