Fundamental Algebraic Geometry

Volume 123

Barbara Fantechi, Lothar Göttsche, Luc Illusie, Steven L. Kleinman, Nitin Nitsure, Angelo Vistoli - Collection Mathematical Surveys and Monographs

350 pages, parution le 28/02/2006

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Résumé

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.

Sommaire

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 scheme of points
- Introduction
- Elementary deformation theory
- Hilbert schemes of points
Grothendieck's existence theorem in formal geometry
- Grothendieck's existence theorem in formal geometry with a letter of Jean-Pierre Serre
The Picard scheme
- The Picard scheme
- Bibliography

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Caractéristiques techniques

	PAPIER
Éditeur(s)	American Mathematical Society (AMS)
Auteur(s)	Barbara Fantechi, Lothar Göttsche, Luc Illusie, Steven L. Kleinman, Nitin Nitsure, Angelo Vistoli
Collection	Mathematical Surveys and Monographs
Parution	28/02/2006
Nb. de pages	350
Format	18,5 x 26
Couverture	Relié
Poids	785g
Intérieur	Noir et Blanc
EAN13	9780821835418
ISBN13	978-0-8218-3541-8