Softcover ISBN:  9780821842454 
Product Code:  SURV/123.S 
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AMS Member Price:  $72.80 
Electronic ISBN:  9781470413507 
Product Code:  SURV/123.S.E 
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Book DetailsMathematical Surveys and MonographsVolume: 123; 2005; 339 ppMSC: 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.ReadershipGraduate 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 nonspecialist, young researchers, and seasoned graduate students. The authors have endeavoured to elaborate Grothendieck's ingenious, epochmaking 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


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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.
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 nonspecialist, young researchers, and seasoned graduate students. The authors have endeavoured to elaborate Grothendieck's ingenious, epochmaking 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