Fundamental algebraic geometry : Grothendieck's FGA explained
著者
書誌事項
Fundamental algebraic geometry : Grothendieck's FGA explained
（Mathematical surveys and monographs, v. 123）
American Mathematical Society, c2005
- : pbk.
- : soft cover
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注記
Includes bibliographical references (p. 323-331) and index
内容説明・目次
- 巻冊次
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: pbk. ISBN 9780821835418
内容説明
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 Seminaire Bourbaki, between 1957 and 1962. He, then, collected these lectures in a series of articles in "Fondements de la geometrie algebrique" (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.
目次
- Preliminary notions
- Contravariant functors
- Fibered categories
- Stacks
- Elementary deformation theory
- Hilbert schemes of points
- Bibliography
- Index
- 巻冊次
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: soft cover ISBN 9780821842454
内容説明
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 Seminaire Bourbaki between 1957 and 1962. He then collected these lectures in a series of articles in Fondements de la geometrie algebrique (commonly known as FGA).
目次
Grothendieck topologies, fibered categories and descent theory: Introduction Preliminary notions Contravariant functors Fibered categories Stacks Construction of Hilbert and Quot schemes: Construction of Hilbert and Quot schemes Local properties and Hilbert schemes of points: Introduction Elementary deformation theory Hilbert schemes of points Grothendieck's existence theorem in formal geometry with a letter of Jean-Pierre Serre: Grothendieck's existence theorem in formal geometry The Picard scheme: The Picard scheme Bibliography Index.
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