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Fundamental Algebraic Geometry: Grothendieck’s FGA Explained
 
Barbara Fantechi SISSA, Trieste, Italy
Lothar Göttsche International Centre for Theoretical Physics, Trieste, Italy
Luc Illusie Université Paris–Sud, Orsay, France
Steven L. Kleiman MIT, Cambridge, MA
Nitin Nitsure Tata Institute of Fundamental Research, Mumbai, India
Angelo Vistoli Università di Bologna, Bologna, Italy
Fundamental Algebraic Geometry
Softcover ISBN:  978-0-8218-4245-4
Product Code:  SURV/123.S
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
This item is temporarily out of stock. Order now and your item will ship as soon as stock becomes available.
Expected availability date: April 29, 2024
eBook ISBN:  978-1-4704-1350-7
Product Code:  SURV/123.S.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-4245-4
eBook: ISBN:  978-1-4704-1350-7
Product Code:  SURV/123.S.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
This item is temporarily out of stock. Order now and your item will ship as soon as stock becomes available.
Expected availability date: April 29, 2024
Fundamental Algebraic Geometry
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Fundamental Algebraic Geometry: Grothendieck’s FGA Explained
Barbara Fantechi SISSA, Trieste, Italy
Lothar Göttsche International Centre for Theoretical Physics, Trieste, Italy
Luc Illusie Université Paris–Sud, Orsay, France
Steven L. Kleiman MIT, Cambridge, MA
Nitin Nitsure Tata Institute of Fundamental Research, Mumbai, India
Angelo Vistoli Università di Bologna, Bologna, Italy
Softcover ISBN:  978-0-8218-4245-4
Product Code:  SURV/123.S
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
This item is temporarily out of stock. Order now and your item will ship as soon as stock becomes available.
Expected availability date: April 29, 2024
eBook ISBN:  978-1-4704-1350-7
Product Code:  SURV/123.S.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-4245-4
eBook ISBN:  978-1-4704-1350-7
Product Code:  SURV/123.S.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
This item is temporarily out of stock. Order now and your item will ship as soon as stock becomes available.
Expected availability date: April 29, 2024
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 1232005; 339 pp
    MSC: Primary 14; 13; 18;

    Alexander Grothendieck's concepts turned out to be astoundingly powerful and productive, truly revolutionizing algebraic geometry. He sketched his new theories in talks given at the Séminaire Bourbaki between 1957 and 1962. He then collected these lectures in a series of articles in Fondements de la géométrie algébrique (commonly known as FGA).

    Much of FGA is now common knowledge. However, some of it is less well known, and only a few geometers are familiar with its full scope. The goal of the current book, which resulted from the 2003 Advanced School in Basic Algebraic Geometry (Trieste, Italy), is to fill in the gaps in Grothendieck's very condensed outline of his theories. The four main themes discussed in the book are descent theory, Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. The authors present complete proofs of the main results, using newer ideas to promote understanding whenever necessary, and drawing connections to later developments.

    With the main prerequisite being a thorough acquaintance with basic scheme theory, this book is a valuable resource for anyone working in algebraic geometry.

    Readership

    Graduate students and research mathematicians interested in algebraic geometry.

  • Table of Contents
     
     
    • Chapters
    • 1. Preliminary notions
    • 2. Contravariant functors
    • 3. Fibered categories
    • 4. Stacks
    • 5. Construction of Hilbert and Quot schemes
    • 6. Elementary deformation theory
    • 7. Hilbert schemes of points
    • 8. Grothendieck’s existence theorem in formal geometry
    • 9. The Picard scheme
  • Additional Material
     
     
  • Reviews
     
     
    • All together, this book must be seen as a highly valuable addition to Grotherndieck's fundamental classic FGA, and as a superb contribution to the propagation of his pioneering work just as well. It is fair to say that, for the first time, the wealth of Grotherndieck's FGA has been made accessible to the entire community of algebraic geometers, including non-specialist, young researchers, and seasoned graduate students. The authors have endeavoured to elaborate Grothendieck's ingenious, epoch-making outlines in the greatest possible clarity and detailedness, with complete proofs given throughout...ought to be in the library of anyone using modern algebraic geometry in his (or her) research.

      Zentralblatt MATH
  • 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: 1232005; 339 pp
MSC: Primary 14; 13; 18;

Alexander Grothendieck's concepts turned out to be astoundingly powerful and productive, truly revolutionizing algebraic geometry. He sketched his new theories in talks given at the Séminaire Bourbaki between 1957 and 1962. He then collected these lectures in a series of articles in Fondements de la géométrie algébrique (commonly known as FGA).

Much of FGA is now common knowledge. However, some of it is less well known, and only a few geometers are familiar with its full scope. The goal of the current book, which resulted from the 2003 Advanced School in Basic Algebraic Geometry (Trieste, Italy), is to fill in the gaps in Grothendieck's very condensed outline of his theories. The four main themes discussed in the book are descent theory, Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. The authors present complete proofs of the main results, using newer ideas to promote understanding whenever necessary, and drawing connections to later developments.

With the main prerequisite being a thorough acquaintance with basic scheme theory, this book is a valuable resource for anyone working in algebraic geometry.

Readership

Graduate students and research mathematicians interested in algebraic geometry.

  • Chapters
  • 1. Preliminary notions
  • 2. Contravariant functors
  • 3. Fibered categories
  • 4. Stacks
  • 5. Construction of Hilbert and Quot schemes
  • 6. Elementary deformation theory
  • 7. Hilbert schemes of points
  • 8. Grothendieck’s existence theorem in formal geometry
  • 9. The Picard scheme
  • All together, this book must be seen as a highly valuable addition to Grotherndieck's fundamental classic FGA, and as a superb contribution to the propagation of his pioneering work just as well. It is fair to say that, for the first time, the wealth of Grotherndieck's FGA has been made accessible to the entire community of algebraic geometers, including non-specialist, young researchers, and seasoned graduate students. The authors have endeavoured to elaborate Grothendieck's ingenious, epoch-making outlines in the greatest possible clarity and detailedness, with complete proofs given throughout...ought to be in the library of anyone using modern algebraic geometry in his (or her) research.

    Zentralblatt MATH
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
Please select which format for which you are requesting permissions.