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A Study in Derived Algebraic Geometry: Volumes I and II
 
Dennis Gaitsgory Harvard University, Cambridge, MA
Nick Rozenblyum University of Chicago, Chicago, IL
A Study in Derived Algebraic Geometry
Softcover ISBN:  978-1-4704-5306-0
Product Code:  SURV/221.S
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
A Study in Derived Algebraic Geometry
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A Study in Derived Algebraic Geometry: Volumes I and II
Dennis Gaitsgory Harvard University, Cambridge, MA
Nick Rozenblyum University of Chicago, Chicago, IL
Softcover ISBN:  978-1-4704-5306-0
Product Code:  SURV/221.S
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 2212017; 969 pp

    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.

    Readership

    Graduate students and researchers interested in new trends in algebraic geometry and representation theory.

    This set contains the following item(s):
  • Additional Material
     
     
  • Reviews
     
     
    • The books are carefully written...and they are not as difficult to read as one might expect from the content. This is mainly due to the many introductions scattered throughout the books, which explain the main ideas of each volume, part or chapter.

      Adrian Langer, Mathematical Reviews
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2212017; 969 pp

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.

Readership

Graduate students and researchers interested in new trends in algebraic geometry and representation theory.

This set contains the following item(s):
  • The books are carefully written...and they are not as difficult to read as one might expect from the content. This is mainly due to the many introductions scattered throughout the books, which explain the main ideas of each volume, part or chapter.

    Adrian Langer, Mathematical Reviews
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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