グロタンディック著「ＦＧＡ」の解説 Fundamental Algebraic Geometry : Grothendieck's FGA Explained (Mathematical Surveys and Monographs)

Fantechl, Barbara/ Göttsche, Lothar/ Illusie, Luc

American Mathematical Society（2006/10発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 339 p.
• 言語 ENG
• 商品コード 9780821842454
• DDC分類 516.35

基本説明

The goal of the current book, which resulted from the 2003 Advanced School in Basic Algebraic Geometry (Italy), is to fill in the gaps in Grothendieck's very condensed outline of his theories.

Full Description

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).

Contents

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.