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Fundamental algebraic geometry: Grothendieck's FGA explained-[djvu]-[Barbara Fantechi; Lothar Göttsche; Luc Illusie; Steven L. Kleiman; Nitin Nitsure; and Angelo Vistoli]

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    书籍信息:
    标题: Fundamental algebraic geometry: Grothendieck's FGA explained
    语言: English
    格式: djvu
    大小: 2.9M
    页数: 352
    年份: 2005
    作者: Barbara Fantechi; Lothar Göttsche; Luc Illusie; Steven L. Kleiman; Nitin Nitsure; and Angelo Vistoli
    系列: Mathematical surveys and monographs 123
    出版社: American Mathematical Society

    简介

    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.

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